diff --git a/src/reader/spirv/enum_converter.cc b/src/reader/spirv/enum_converter.cc
index 26aba0ab06..b52af7bdda 100644
--- a/src/reader/spirv/enum_converter.cc
+++ b/src/reader/spirv/enum_converter.cc
@@ -38,7 +38,7 @@ ast::PipelineStage EnumConverter::ToPipelineStage(SpvExecutionModel model) {
   return ast::PipelineStage::kNone;
 }
 
-ast::StorageClass EnumConverter::ToStorageClass(SpvStorageClass sc) {
+ast::StorageClass EnumConverter::ToStorageClass(const SpvStorageClass sc) {
   switch (sc) {
     case SpvStorageClassInput:
       return ast::StorageClass::kInput;
diff --git a/src/reader/spirv/enum_converter.h b/src/reader/spirv/enum_converter.h
index ca7516ab09..cdf922ff69 100644
--- a/src/reader/spirv/enum_converter.h
+++ b/src/reader/spirv/enum_converter.h
@@ -44,7 +44,7 @@ class EnumConverter {
   /// On failure, logs an error and returns kNone
   /// @param sc the SPIR-V storage class
   /// @returns a Tint AST storage class
-  ast::StorageClass ToStorageClass(SpvStorageClass sc);
+  ast::StorageClass ToStorageClass(const SpvStorageClass sc);
 
   /// Converts a SPIR-V Builtin value a Tint Builtin.
   /// On failure, logs an error and returns kNone
diff --git a/src/reader/spirv/function.cc b/src/reader/spirv/function.cc
index f62c967f0b..6f8de075bc 100644
--- a/src/reader/spirv/function.cc
+++ b/src/reader/spirv/function.cc
@@ -631,7 +631,10 @@ bool FunctionEmitter::EmitBody() {
     return false;
   }
 
-  RegisterValuesNeedingNamedOrHoistedDefinition();
+  if (!RegisterLocallyDefinedValues()) {
+    return false;
+  }
+  FindValuesNeedingNamedOrHoistedDefinition();
 
   if (!EmitFunctionVariables()) {
     return false;
@@ -2419,10 +2422,10 @@ bool FunctionEmitter::EmitStatementsInBasicBlock(const BlockInfo& block_info,
   for (auto id : sorted_by_index(block_info.hoisted_ids)) {
     const auto* def_inst = def_use_mgr_->GetDef(id);
     assert(def_inst);
-    AddStatement(
-        std::make_unique<ast::VariableDeclStatement>(parser_impl_.MakeVariable(
-            id, ast::StorageClass::kFunction,
-            parser_impl_.ConvertType(def_inst->type_id()))));
+    auto* ast_type =
+        RemapStorageClass(parser_impl_.ConvertType(def_inst->type_id()), id);
+    AddStatement(std::make_unique<ast::VariableDeclStatement>(
+        parser_impl_.MakeVariable(id, ast::StorageClass::kFunction, ast_type)));
     // Save this as an already-named value.
     identifier_values_.insert(id);
   }
@@ -2580,12 +2583,14 @@ bool FunctionEmitter::EmitStatement(const spvtools::opt::Instruction& inst) {
       expr.type = expr.type->AsPointer()->type();
       return EmitConstDefOrWriteToHoistedVar(inst, std::move(expr));
     }
-    case SpvOpCopyObject:
+    case SpvOpCopyObject: {
       // Arguably, OpCopyObject is purely combinatorial. On the other hand,
       // it exists to make a new name for something. So we choose to make
       // a new named constant definition.
-      return EmitConstDefOrWriteToHoistedVar(
-          inst, MakeExpression(inst.GetSingleWordInOperand(0)));
+      auto expr = MakeExpression(inst.GetSingleWordInOperand(0));
+      expr.type = RemapStorageClass(expr.type, result_id);
+      return EmitConstDefOrWriteToHoistedVar(inst, std::move(expr));
+    }
     case SpvOpPhi: {
       // Emit a read from the associated state variable.
       auto expr = TypedExpression(
@@ -2754,7 +2759,6 @@ TypedExpression FunctionEmitter::MakeAccessChain(
   // ever-deeper nested indexing expressions. Start off with an expression
   // for the base, and then bury that inside nested indexing expressions.
   TypedExpression current_expr(MakeOperand(inst, 0));
-
   const auto constants = constant_mgr_->GetOperandConstants(&inst);
   static const char* swizzles[] = {"x", "y", "z", "w"};
 
@@ -2803,9 +2807,10 @@ TypedExpression FunctionEmitter::MakeAccessChain(
       // Skip past the member index that gets us to Position.
       first_index = first_index + 1;
       // Replace the gl_PerVertex reference with the gl_Position reference
+      ptr_ty_id = builtin_position_info.member_pointer_type_id;
       current_expr.expr =
           std::make_unique<ast::IdentifierExpression>(namer_.Name(base_id));
-      ptr_ty_id = builtin_position_info.member_pointer_type_id;
+      current_expr.type = parser_impl_.ConvertType(ptr_ty_id);
     }
   }
 
@@ -2815,6 +2820,7 @@ TypedExpression FunctionEmitter::MakeAccessChain(
            << " base pointer is not of pointer type";
     return {};
   }
+  SpvStorageClass storage_class = ptr_type->AsPointer()->storage_class();
   const auto* pointee_type = ptr_type->AsPointer()->pointee_type();
   for (uint32_t index = first_index; index < num_in_operands; ++index) {
     const auto* index_const =
@@ -2904,9 +2910,13 @@ TypedExpression FunctionEmitter::MakeAccessChain(
                << type_mgr_->GetId(pointee_type) << " " << pointee_type->str();
         return {};
     }
-    current_expr.reset(TypedExpression(
-        parser_impl_.ConvertType(type_mgr_->GetId(pointee_type)),
-        std::move(next_expr)));
+    const auto pointee_type_id = type_mgr_->GetId(pointee_type);
+    const auto pointer_type_id =
+        type_mgr_->FindPointerToType(pointee_type_id, storage_class);
+    auto* ast_pointer_type = parser_impl_.ConvertType(pointer_type_id);
+    assert(ast_pointer_type);
+    assert(ast_pointer_type->IsPointer);
+    current_expr.reset(TypedExpression(ast_pointer_type, std::move(next_expr)));
   }
   return current_expr;
 }
@@ -3074,7 +3084,7 @@ TypedExpression FunctionEmitter::MakeVectorShuffle(
                            result_type, std::move(values))};
 }
 
-void FunctionEmitter::RegisterValuesNeedingNamedOrHoistedDefinition() {
+bool FunctionEmitter::RegisterLocallyDefinedValues() {
   // Create a DefInfo for each value definition in this function.
   size_t index = 0;
   for (auto block_id : block_order_) {
@@ -3087,9 +3097,72 @@ void FunctionEmitter::RegisterValuesNeedingNamedOrHoistedDefinition() {
       }
       def_info_[result_id] = std::make_unique<DefInfo>(inst, block_pos, index);
       index++;
+
+      // Determine storage class for pointer values. Do this in order because
+      // we might rely on the storage class for a previously-visited definition.
+      // Logical pointers can't be transmitted through OpPhi, so remaining
+      // pointer definitions are SSA values, and their definitions must be
+      // visited before their uses.
+      auto& storage_class = def_info_[result_id]->storage_class;
+      const auto* type = type_mgr_->GetType(inst.type_id());
+      if (type && type->AsPointer()) {
+        const auto* ast_type = parser_impl_.ConvertType(inst.type_id());
+        if (ast_type && ast_type->AsPointer()) {
+          storage_class = ast_type->AsPointer()->storage_class();
+        }
+        switch (inst.opcode()) {
+          case SpvOpUndef:
+          case SpvOpVariable:
+            // Keep the default decision based on the result type.
+            break;
+          case SpvOpAccessChain:
+          case SpvOpCopyObject:
+            // Inherit from the first operand. We need this so we can pick up
+            // a remapped storage buffer.
+            storage_class =
+                GetStorageClassForPointerValue(inst.GetSingleWordInOperand(0));
+            break;
+          default:
+            return Fail() << "pointer defined in function from unknown opcode: "
+                          << inst.PrettyPrint();
+        }
+      }
     }
   }
+  return true;
+}
 
+ast::StorageClass FunctionEmitter::GetStorageClassForPointerValue(uint32_t id) {
+  auto where = def_info_.find(id);
+  if (where != def_info_.end()) {
+    return where->second.get()->storage_class;
+  }
+  const auto type_id = def_use_mgr_->GetDef(id)->type_id();
+  if (type_id) {
+    auto* ast_type = parser_impl_.ConvertType(type_id);
+    if (ast_type && ast_type->IsPointer()) {
+      return ast_type->AsPointer()->storage_class();
+    }
+  }
+  return ast::StorageClass::kNone;
+}
+
+ast::type::Type* FunctionEmitter::RemapStorageClass(ast::type::Type* type,
+                                                    uint32_t result_id) {
+  if (type->IsPointer()) {
+    // Remap an old-style storage buffer pointer to a new-style storage
+    // buffer pointer.
+    const auto* ast_ptr_type = type->AsPointer();
+    const auto sc = GetStorageClassForPointerValue(result_id);
+    if (ast_ptr_type->storage_class() != sc) {
+      return parser_impl_.context().type_mgr().Get(
+          std::make_unique<ast::type::PointerType>(ast_ptr_type->type(), sc));
+    }
+  }
+  return type;
+}
+
+void FunctionEmitter::FindValuesNeedingNamedOrHoistedDefinition() {
   // Mark vector operands of OpVectorShuffle as needing a named definition,
   // but only if they are defined in this function as well.
   for (auto& id_def_info_pair : def_info_) {
diff --git a/src/reader/spirv/function.h b/src/reader/spirv/function.h
index 476818fe1b..e3bde3a465 100644
--- a/src/reader/spirv/function.h
+++ b/src/reader/spirv/function.h
@@ -33,6 +33,7 @@
 #include "src/ast/expression.h"
 #include "src/ast/module.h"
 #include "src/ast/statement.h"
+#include "src/ast/storage_class.h"
 #include "src/reader/spirv/construct.h"
 #include "src/reader/spirv/fail_stream.h"
 #include "src/reader/spirv/namer.h"
@@ -192,7 +193,7 @@ inline std::ostream& operator<<(std::ostream& o, const BlockInfo& bi) {
 
 /// Bookkeeping info for a SPIR-V ID defined in the function.
 /// This will be valid for result IDs for:
-/// - instructions that are not OpLabel, OpVariable, and OpFunctionParameter
+/// - instructions that are not OpLabel, and not OpFunctionParameter
 /// - are defined in a basic block visited in the block-order for the function.
 struct DefInfo {
   /// Constructor.
@@ -243,8 +244,15 @@ struct DefInfo {
 
   /// If the definition is an OpPhi, then |phi_var| is the name of the
   /// variable that stores the value carried from parent basic blocks into
-  // the basic block containing the OpPhi. Otherwise this is the empty string.
+  /// the basic block containing the OpPhi. Otherwise this is the empty string.
   std::string phi_var;
+
+  /// The storage class to use for this value, if it is of pointer type.
+  /// This is required to carry a stroage class override from a storage
+  /// buffer expressed in the old style (with Uniform storage class)
+  /// that needs to be remapped to StorageBuffer storage class.
+  /// This is kNone for non-pointers.
+  ast::StorageClass storage_class = ast::StorageClass::kNone;
 };
 
 inline std::ostream& operator<<(std::ostream& o, const DefInfo& di) {
@@ -254,8 +262,11 @@ inline std::ostream& operator<<(std::ostream& o, const DefInfo& di) {
     << " last_use_pos: " << di.last_use_pos << " requires_named_const_def: "
     << (di.requires_named_const_def ? "true" : "false")
     << " requires_hoisted_def: " << (di.requires_hoisted_def ? "true" : "false")
-    << " phi_var: '" << di.phi_var << "'"
-    << "}";
+    << " phi_var: '" << di.phi_var << "'";
+  if (di.storage_class != ast::StorageClass::kNone) {
+    o << " sc:" << int(di.storage_class);
+  }
+  o << "}";
   return o;
 }
 
@@ -367,7 +378,24 @@ class FunctionEmitter {
   /// @returns false if bad nesting has been detected.
   bool FindIfSelectionInternalHeaders();
 
-  /// Record the SPIR-V IDs of non-constants that should get a 'const'
+  /// Creates a DefInfo record for each locally defined SPIR-V ID.
+  /// Populates the |def_info_| mapping with basic results.
+  /// @returns false on failure
+  bool RegisterLocallyDefinedValues();
+
+  /// Returns the Tint storage class for the given SPIR-V ID that is a
+  /// pointer value.
+  /// @returns the storage class
+  ast::StorageClass GetStorageClassForPointerValue(uint32_t id);
+
+  /// Remaps the storage class for the type of a locally-defined value,
+  /// if necessary. If it's not a pointer type, or if its storage class
+  /// already matches, then the result is a copy of the |type| argument.
+  /// @param type the AST type
+  /// @param result_id the SPIR-V ID for the locally defined value
+  ast::type::Type* RemapStorageClass(ast::type::Type* type, uint32_t result_id);
+
+  /// Marks locally defined values when they should get a 'const'
   /// definition in WGSL, or a 'var' definition at an outer scope.
   /// This occurs in several cases:
   ///  - When a SPIR-V instruction might use the dynamically computed value
@@ -382,8 +410,8 @@ class FunctionEmitter {
   ///  - When a definition is in a construct that does not enclose all the
   ///    uses.  In this case the definition's |requires_hoisted_def| property
   ///    is set to true.
-  /// Populates the |def_info_| mapping.
-  void RegisterValuesNeedingNamedOrHoistedDefinition();
+  /// Updates the |def_info_| mapping.
+  void FindValuesNeedingNamedOrHoistedDefinition();
 
   /// Emits declarations of function variables.
   /// @returns false if emission failed.
diff --git a/src/reader/spirv/function_composite_test.cc b/src/reader/spirv/function_composite_test.cc
index f3caa245d7..b3997018aa 100644
--- a/src/reader/spirv/function_composite_test.cc
+++ b/src/reader/spirv/function_composite_test.cc
@@ -287,10 +287,10 @@ TEST_F(SpvParserTest_CompositeExtract, Vector_IndexTooBigError) {
 TEST_F(SpvParserTest_CompositeExtract, Matrix) {
   const auto assembly = Preamble() + R"(
      %ptr = OpTypePointer Function %m3v2float
-     %var = OpVariable %ptr Function
 
      %100 = OpFunction %void None %voidfn
      %entry = OpLabel
+     %var = OpVariable %ptr Function
      %1 = OpLoad %m3v2float %var
      %2 = OpCompositeExtract %v2float %1 2
      OpReturn
@@ -318,10 +318,10 @@ TEST_F(SpvParserTest_CompositeExtract, Matrix) {
 TEST_F(SpvParserTest_CompositeExtract, Matrix_IndexTooBigError) {
   const auto assembly = Preamble() + R"(
      %ptr = OpTypePointer Function %m3v2float
-     %var = OpVariable %ptr Function
 
      %100 = OpFunction %void None %voidfn
      %entry = OpLabel
+     %var = OpVariable %ptr Function
      %1 = OpLoad %m3v2float %var
      %2 = OpCompositeExtract %v2float %1 3
      OpReturn
@@ -338,10 +338,10 @@ TEST_F(SpvParserTest_CompositeExtract, Matrix_IndexTooBigError) {
 TEST_F(SpvParserTest_CompositeExtract, Matrix_Vector) {
   const auto assembly = Preamble() + R"(
      %ptr = OpTypePointer Function %m3v2float
-     %var = OpVariable %ptr Function
 
      %100 = OpFunction %void None %voidfn
      %entry = OpLabel
+     %var = OpVariable %ptr Function
      %1 = OpLoad %m3v2float %var
      %2 = OpCompositeExtract %float %1 2 1
      OpReturn
@@ -372,10 +372,10 @@ TEST_F(SpvParserTest_CompositeExtract, Matrix_Vector) {
 TEST_F(SpvParserTest_CompositeExtract, Array) {
   const auto assembly = Preamble() + R"(
      %ptr = OpTypePointer Function %a_u_5
-     %var = OpVariable %ptr Function
 
      %100 = OpFunction %void None %voidfn
      %entry = OpLabel
+     %var = OpVariable %ptr Function
      %1 = OpLoad %a_u_5 %var
      %2 = OpCompositeExtract %uint %1 3
      OpReturn
@@ -404,10 +404,10 @@ TEST_F(SpvParserTest_CompositeExtract, RuntimeArray_IsError) {
   const auto assembly = Preamble() + R"(
      %rtarr = OpTypeRuntimeArray %uint
      %ptr = OpTypePointer Function %rtarr
-     %var = OpVariable %ptr Function
 
      %100 = OpFunction %void None %voidfn
      %entry = OpLabel
+     %var = OpVariable %ptr Function
      %1 = OpLoad %rtarr %var
      %2 = OpCompositeExtract %uint %1 3
      OpReturn
@@ -423,10 +423,10 @@ TEST_F(SpvParserTest_CompositeExtract, RuntimeArray_IsError) {
 TEST_F(SpvParserTest_CompositeExtract, Struct) {
   const auto assembly = Preamble() + R"(
      %ptr = OpTypePointer Function %s_v2f_u_i
-     %var = OpVariable %ptr Function
 
      %100 = OpFunction %void None %voidfn
      %entry = OpLabel
+     %var = OpVariable %ptr Function
      %1 = OpLoad %s_v2f_u_i %var
      %2 = OpCompositeExtract %int %1 2
      OpReturn
@@ -454,10 +454,10 @@ TEST_F(SpvParserTest_CompositeExtract, Struct) {
 TEST_F(SpvParserTest_CompositeExtract, Struct_IndexTooBigError) {
   const auto assembly = Preamble() + R"(
      %ptr = OpTypePointer Function %s_v2f_u_i
-     %var = OpVariable %ptr Function
 
      %100 = OpFunction %void None %voidfn
      %entry = OpLabel
+     %var = OpVariable %ptr Function
      %1 = OpLoad %s_v2f_u_i %var
      %2 = OpCompositeExtract %int %1 40
      OpReturn
@@ -476,10 +476,10 @@ TEST_F(SpvParserTest_CompositeExtract, Struct_Array_Matrix_Vector) {
      %a_mat = OpTypeArray %m3v2float %uint_3
      %s = OpTypeStruct %uint %a_mat
      %ptr = OpTypePointer Function %s
-     %var = OpVariable %ptr Function
 
      %100 = OpFunction %void None %voidfn
      %entry = OpLabel
+     %var = OpVariable %ptr Function
      %1 = OpLoad %s %var
      %2 = OpCompositeExtract %float %1 1 2 0 1
      OpReturn
@@ -553,10 +553,10 @@ VariableDeclStatement{
 TEST_F(SpvParserTest_CopyObject, Pointer) {
   const auto assembly = Preamble() + R"(
      %ptr = OpTypePointer Function %uint
-     %10 = OpVariable %ptr Function
 
      %100 = OpFunction %void None %voidfn
      %entry = OpLabel
+     %10 = OpVariable %ptr Function
      %1 = OpCopyObject %ptr %10
      %2 = OpCopyObject %ptr %1
      OpReturn
diff --git a/src/reader/spirv/function_memory_test.cc b/src/reader/spirv/function_memory_test.cc
index 5bdfb2c96b..662e9cb109 100644
--- a/src/reader/spirv/function_memory_test.cc
+++ b/src/reader/spirv/function_memory_test.cc
@@ -708,6 +708,245 @@ TEST_F(SpvParserTest, EmitStatement_AccessChain_InvalidPointeeType) {
               HasSubstr("Access chain with unknown pointee type %60 void"));
 }
 
+std::string OldStorageBufferPreamble() {
+  return R"(
+     OpName %myvar "myvar"
+
+     OpDecorate %struct BufferBlock
+     OpMemberDecorate %struct 0 Offset 0
+     OpMemberDecorate %struct 1 Offset 4
+     OpDecorate %arr ArrayStride 4
+
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %uint = OpTypeInt 32 0
+
+     %uint_0 = OpConstant %uint 0
+     %uint_1 = OpConstant %uint 1
+
+     %arr = OpTypeRuntimeArray %uint
+     %struct = OpTypeStruct %uint %arr
+     %ptr_struct = OpTypePointer Uniform %struct
+     %ptr_uint = OpTypePointer Uniform %uint
+
+     %myvar = OpVariable %ptr_struct Uniform
+  )";
+}
+
+TEST_F(SpvParserTest, RemapStorageBuffer_TypesAndVarDeclarations) {
+  // Enusure we get the right module-scope declaration.  This tests translation
+  // of the structure type, arrays of the structure, pointers to them, and
+  // OpVariable of these.
+  const auto assembly = OldStorageBufferPreamble();
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions())
+      << assembly << p->error();
+  const auto module_str = p->module().to_str();
+  EXPECT_THAT(module_str, HasSubstr(R"(
+  Variable{
+    myvar
+    storage_buffer
+    __alias_S__struct_S
+  }
+RTArr -> __array__u32_stride_4
+S -> __struct_S)"));
+}
+
+TEST_F(SpvParserTest,
+       RemapStorageBuffer_ThroughAccessChain_NonCascaded) {
+  const auto assembly = OldStorageBufferPreamble() + R"(
+  %100 = OpFunction %void None %voidfn
+  %entry = OpLabel
+
+  ; the scalar element
+  %1 = OpAccessChain %ptr_uint %myvar %uint_0
+  OpStore %1 %uint_0
+
+  ; element in the runtime array
+  %2 = OpAccessChain %ptr_uint %myvar %uint_1 %uint_1
+  OpStore %2 %uint_0
+
+  OpReturn
+  OpFunctionEnd
+)";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModule()) << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_TRUE(fe.EmitBody()) << p->error();
+  EXPECT_THAT(ToString(fe.ast_body()), HasSubstr(R"(Assignment{
+  MemberAccessor{
+    Identifier{myvar}
+    Identifier{field0}
+  }
+  ScalarConstructor{0}
+}
+Assignment{
+  ArrayAccessor{
+    MemberAccessor{
+      Identifier{myvar}
+      Identifier{field1}
+    }
+    ScalarConstructor{1}
+  }
+  ScalarConstructor{0}
+})")) << ToString(fe.ast_body())
+      << p->error();
+}
+
+TEST_F(SpvParserTest, RemapStorageBuffer_ThroughAccessChain_Cascaded) {
+  const auto assembly = OldStorageBufferPreamble() + R"(
+  %ptr_rtarr = OpTypePointer Uniform %arr
+  %100 = OpFunction %void None %voidfn
+  %entry = OpLabel
+
+  ; get the runtime array
+  %1 = OpAccessChain %ptr_rtarr %myvar %uint_1
+  ; now an element in it
+  %2 = OpAccessChain %ptr_uint %1 %uint_1
+  OpStore %2 %uint_0
+
+  OpReturn
+  OpFunctionEnd
+)";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModule()) << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_TRUE(fe.EmitBody()) << p->error();
+  EXPECT_THAT(ToString(fe.ast_body()), HasSubstr(R"(Assignment{
+  ArrayAccessor{
+    MemberAccessor{
+      Identifier{myvar}
+      Identifier{field1}
+    }
+    ScalarConstructor{1}
+  }
+  ScalarConstructor{0}
+})")) << ToString(fe.ast_body())
+      << p->error();
+}
+
+TEST_F(SpvParserTest,
+       RemapStorageBuffer_ThroughCopyObject_WithoutHoisting) {
+  // Generates a const declaration directly.
+  // We have to do a bunch of storage class tracking for locally
+  // defined values in order to get the right pointer-to-storage-buffer
+  // value type for the const declration.
+  const auto assembly = OldStorageBufferPreamble() + R"(
+  %100 = OpFunction %void None %voidfn
+  %entry = OpLabel
+
+  %1 = OpAccessChain %ptr_uint %myvar %uint_1 %uint_1
+  %2 = OpCopyObject %ptr_uint %1
+  OpStore %2 %uint_0
+
+  OpReturn
+  OpFunctionEnd
+)";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModule()) << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_TRUE(fe.EmitBody()) << p->error();
+  EXPECT_THAT(ToString(fe.ast_body()), HasSubstr(R"(VariableDeclStatement{
+  Variable{
+    x_2
+    none
+    __ptr_storage_buffer__u32
+    {
+      ArrayAccessor{
+        MemberAccessor{
+          Identifier{myvar}
+          Identifier{field1}
+        }
+        ScalarConstructor{1}
+      }
+    }
+  }
+}
+Assignment{
+  Identifier{x_2}
+  ScalarConstructor{0}
+})")) << ToString(fe.ast_body())
+      << p->error();
+}
+
+TEST_F(SpvParserTest, RemapStorageBuffer_ThroughCopyObject_WithHoisting) {
+  // Like the previous test, but the declaration for the copy-object
+  // has its declaration hoisted.
+  const auto assembly = OldStorageBufferPreamble() + R"(
+  %bool = OpTypeBool
+  %cond = OpConstantTrue %bool
+
+  %100 = OpFunction %void None %voidfn
+
+  %entry = OpLabel
+  OpSelectionMerge %99 None
+  OpBranchConditional %cond %20 %30
+
+  %20 = OpLabel
+  %1 = OpAccessChain %ptr_uint %myvar %uint_1 %uint_1
+  ; this definintion dominates the use in %99
+  %2 = OpCopyObject %ptr_uint %1
+  OpBranch %99
+
+  %30 = OpLabel
+  OpReturn
+
+  %99 = OpLabel
+  OpStore %2 %uint_0
+  OpReturn
+
+  OpFunctionEnd
+)";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModule()) << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_TRUE(fe.EmitBody()) << p->error();
+  EXPECT_THAT(ToString(fe.ast_body()), Eq(R"(VariableDeclStatement{
+  Variable{
+    x_2
+    function
+    __ptr_storage_buffer__u32
+  }
+}
+If{
+  (
+    ScalarConstructor{true}
+  )
+  {
+    Assignment{
+      Identifier{x_2}
+      ArrayAccessor{
+        MemberAccessor{
+          Identifier{myvar}
+          Identifier{field1}
+        }
+        ScalarConstructor{1}
+      }
+    }
+  }
+}
+Else{
+  {
+    Return{}
+  }
+}
+Assignment{
+  Identifier{x_2}
+  ScalarConstructor{0}
+}
+Return{}
+)")) << ToString(fe.ast_body())
+     << p->error();
+}
+
+TEST_F(SpvParserTest, DISABLED_RemapStorageBuffer_ThroughFunctionCall) {
+  // TODO(dneto): Blocked on OpFunctionCall support.
+  // We might need this for passing pointers into atomic builtins.
+}
+TEST_F(SpvParserTest, DISABLED_RemapStorageBuffer_ThroughFunctionParameter) {
+  // TODO(dneto): Blocked on OpFunctionCall support.
+}
+
 }  // namespace
 }  // namespace spirv
 }  // namespace reader
diff --git a/src/reader/spirv/parser_impl.cc b/src/reader/spirv/parser_impl.cc
index 69fe861240..9c1a158b8b 100644
--- a/src/reader/spirv/parser_impl.cc
+++ b/src/reader/spirv/parser_impl.cc
@@ -65,6 +65,7 @@
 #include "src/ast/variable.h"
 #include "src/ast/variable_decl_statement.h"
 #include "src/ast/variable_decoration.h"
+#include "src/reader/spirv/enum_converter.h"
 #include "src/reader/spirv/function.h"
 #include "src/type_manager.h"
 
@@ -612,7 +613,8 @@ ast::type::Type* ParserImpl::ConvertType(
 
 ast::type::Type* ParserImpl::ConvertType(
     const spvtools::opt::analysis::Array* arr_ty) {
-  auto* ast_elem_ty = ConvertType(type_mgr_->GetId(arr_ty->element_type()));
+  const auto elem_type_id = type_mgr_->GetId(arr_ty->element_type());
+  auto* ast_elem_ty = ConvertType(elem_type_id);
   if (ast_elem_ty == nullptr) {
     return nullptr;
   }
@@ -648,6 +650,9 @@ ast::type::Type* ParserImpl::ConvertType(
   if (!ApplyArrayDecorations(arr_ty, ast_type.get())) {
     return nullptr;
   }
+  if (remap_buffer_block_type_.count(elem_type_id)) {
+    remap_buffer_block_type_.insert(type_mgr_->GetId(arr_ty));
+  }
   return ctx_.type_mgr().Get(std::move(ast_type));
 }
 
@@ -684,9 +689,17 @@ ast::type::Type* ParserImpl::ConvertType(
   // Compute the struct decoration.
   auto struct_decorations = this->GetDecorationsFor(type_id);
   auto ast_struct_decoration = ast::StructDecoration::kNone;
-  if (struct_decorations.size() == 1 &&
-      struct_decorations[0][0] == SpvDecorationBlock) {
-    ast_struct_decoration = ast::StructDecoration::kBlock;
+  if (struct_decorations.size() == 1) {
+    const auto decoration = struct_decorations[0][0];
+    if (decoration == SpvDecorationBlock) {
+      ast_struct_decoration = ast::StructDecoration::kBlock;
+    } else if (decoration == SpvDecorationBufferBlock) {
+      ast_struct_decoration = ast::StructDecoration::kBlock;
+      remap_buffer_block_type_.insert(type_id);
+    } else {
+      Fail() << "struct with ID " << type_id
+             << " has unrecognized decoration: " << int(decoration);
+    }
   } else if (struct_decorations.size() > 1) {
     Fail() << "can't handle a struct with more than one decoration: struct "
            << type_id << " has " << struct_decorations.size();
@@ -751,26 +764,28 @@ ast::type::Type* ParserImpl::ConvertType(
   // Set the struct name before registering it.
   namer_.SuggestSanitizedName(type_id, "S");
   ast_struct_type->set_name(namer_.GetName(type_id));
-  return ctx_.type_mgr().Get(std::move(ast_struct_type));
+  auto* result = ctx_.type_mgr().Get(std::move(ast_struct_type));
+  return result;
 }
 
 ast::type::Type* ParserImpl::ConvertType(
     uint32_t type_id,
     const spvtools::opt::analysis::Pointer*) {
   const auto* inst = def_use_mgr_->GetDef(type_id);
-  const auto pointee_ty_id = inst->GetSingleWordInOperand(1);
+  const auto pointee_type_id = inst->GetSingleWordInOperand(1);
   const auto storage_class = SpvStorageClass(inst->GetSingleWordInOperand(0));
-  if (pointee_ty_id == builtin_position_.struct_type_id) {
+  if (pointee_type_id == builtin_position_.struct_type_id) {
     builtin_position_.pointer_type_id = type_id;
     builtin_position_.storage_class = storage_class;
     return nullptr;
   }
-  auto* ast_elem_ty = ConvertType(pointee_ty_id);
+  auto* ast_elem_ty = ConvertType(pointee_type_id);
   if (ast_elem_ty == nullptr) {
     Fail() << "SPIR-V pointer type with ID " << type_id
-           << " has invalid pointee type " << pointee_ty_id;
+           << " has invalid pointee type " << pointee_type_id;
     return nullptr;
   }
+
   auto ast_storage_class = enum_converter_.ToStorageClass(storage_class);
   if (ast_storage_class == ast::StorageClass::kNone) {
     Fail() << "SPIR-V pointer type with ID " << type_id
@@ -778,6 +793,11 @@ ast::type::Type* ParserImpl::ConvertType(
            << static_cast<uint32_t>(storage_class);
     return nullptr;
   }
+  if (ast_storage_class == ast::StorageClass::kUniform &&
+      remap_buffer_block_type_.count(pointee_type_id)) {
+    ast_storage_class = ast::StorageClass::kStorageBuffer;
+    remap_buffer_block_type_.insert(type_id);
+  }
   return ctx_.type_mgr().Get(
       std::make_unique<ast::type::PointerType>(ast_elem_ty, ast_storage_class));
 }
@@ -854,7 +874,8 @@ bool ParserImpl::EmitModuleScopeVariables() {
       continue;
     }
     const auto& var = type_or_value;
-    const auto spirv_storage_class = var.GetSingleWordInOperand(0);
+    const auto spirv_storage_class =
+        SpvStorageClass(var.GetSingleWordInOperand(0));
 
     uint32_t type_id = var.type_id();
     if ((type_id == builtin_position_.pointer_type_id) &&
@@ -864,9 +885,21 @@ bool ParserImpl::EmitModuleScopeVariables() {
       builtin_position_.per_vertex_var_id = var.result_id();
       continue;
     }
-
-    auto ast_storage_class = enum_converter_.ToStorageClass(
-        static_cast<SpvStorageClass>(spirv_storage_class));
+    switch (enum_converter_.ToStorageClass(spirv_storage_class)) {
+      case ast::StorageClass::kInput:
+      case ast::StorageClass::kOutput:
+      case ast::StorageClass::kUniform:
+      case ast::StorageClass::kUniformConstant:
+      case ast::StorageClass::kStorageBuffer:
+      case ast::StorageClass::kImage:
+      case ast::StorageClass::kWorkgroup:
+      case ast::StorageClass::kPrivate:
+        break;
+      default:
+        return Fail() << "invalid SPIR-V storage class "
+                      << int(spirv_storage_class)
+                      << " for module scope variable: " << var.PrettyPrint();
+    }
     if (!success_) {
       return false;
     }
@@ -881,6 +914,7 @@ bool ParserImpl::EmitModuleScopeVariables() {
                     << " has non-pointer type " << var.type_id();
     }
     auto* ast_store_type = ast_type->AsPointer()->type();
+    auto ast_storage_class = ast_type->AsPointer()->storage_class();
     auto ast_var =
         MakeVariable(var.result_id(), ast_storage_class, ast_store_type);
     if (var.NumInOperands() > 1) {
diff --git a/src/reader/spirv/parser_impl.h b/src/reader/spirv/parser_impl.h
index 6fc60a5bff..d304aad57f 100644
--- a/src/reader/spirv/parser_impl.h
+++ b/src/reader/spirv/parser_impl.h
@@ -89,6 +89,11 @@ class ParserImpl : Reader {
   /// @returns true if the parse was successful, false otherwise.
   bool Parse() override;
 
+  /// @returns the Tint context.
+  Context& context() {
+    return ctx_;  // Inherited from Reader
+  }
+
   /// @returns the module. The module in the parser will be reset after this.
   ast::Module module() override;
 
@@ -439,6 +444,16 @@ class ParserImpl : Reader {
   //    [[position]] var<in> gl_Position : vec4<f32>;
   // The builtin variable was detected if and only if the struct_id is non-zero.
   BuiltInPositionInfo builtin_position_;
+
+  // SPIR-V type IDs that are either:
+  // - a struct type decorated by BufferBlock
+  // - an array, runtime array containing one of these
+  // - a pointer type to one of these
+  // These are the types "enclosing" a buffer block with the old style
+  // representation: using Uniform storage class and BufferBlock decoration
+  // on the struct.  The new style is to use the StorageBuffer storage class
+  // and Block decoration.
+  std::unordered_set<uint32_t> remap_buffer_block_type_;
 };
 
 }  // namespace spirv
diff --git a/src/reader/spirv/parser_impl_module_var_test.cc b/src/reader/spirv/parser_impl_module_var_test.cc
index da57fd8a70..83895af7f8 100644
--- a/src/reader/spirv/parser_impl_module_var_test.cc
+++ b/src/reader/spirv/parser_impl_module_var_test.cc
@@ -70,7 +70,7 @@ TEST_F(SpvParserTest, ModuleScopeVar_NoVar) {
   EXPECT_THAT(module_ast, Not(HasSubstr("Variable")));
 }
 
-TEST_F(SpvParserTest, ModuleScopeVar_BadStorageClass) {
+TEST_F(SpvParserTest, ModuleScopeVar_BadStorageClass_NotAWebGPUStorageClass) {
   auto* p = parser(test::Assemble(R"(
     %float = OpTypeFloat 32
     %ptr = OpTypePointer CrossWorkgroup %float
@@ -84,6 +84,22 @@ TEST_F(SpvParserTest, ModuleScopeVar_BadStorageClass) {
   EXPECT_THAT(p->error(), HasSubstr("unknown SPIR-V storage class: 5"));
 }
 
+TEST_F(SpvParserTest, ModuleScopeVar_BadStorageClass_Function) {
+  auto* p = parser(test::Assemble(R"(
+    %float = OpTypeFloat 32
+    %ptr = OpTypePointer Function %float
+    %52 = OpVariable %ptr Function
+  )"));
+  EXPECT_TRUE(p->BuildInternalModule());
+  // Normally we should run ParserImpl::RegisterTypes before emitting
+  // variables. But defensive coding in EmitModuleScopeVariables lets
+  // us catch this error.
+  EXPECT_FALSE(p->EmitModuleScopeVariables()) << p->error();
+  EXPECT_THAT(p->error(),
+              HasSubstr("invalid SPIR-V storage class 7 for module scope "
+                        "variable: %52 = OpVariable %2 Function"));
+}
+
 TEST_F(SpvParserTest, ModuleScopeVar_BadPointerType) {
   auto* p = parser(test::Assemble(R"(
     %float = OpTypeFloat 32