diff --git a/src/reader/spirv/function_memory_test.cc b/src/reader/spirv/function_memory_test.cc
index ce09c04e78..e1c6dabfd6 100644
--- a/src/reader/spirv/function_memory_test.cc
+++ b/src/reader/spirv/function_memory_test.cc
@@ -1199,6 +1199,9 @@ Assignment{
   }
   ScalarConstructor[not set]{0u}
 })")) << p->error();
+
+  p->SkipDumpingPending(
+      "crbug.com/tint/1041 track access mode in spirv-reader parser type");
 }
 
 TEST_F(SpvParserMemoryTest, RemapStorageBuffer_ThroughCopyObject_WithHoisting) {
diff --git a/src/reader/spirv/parser_impl_import_test.cc b/src/reader/spirv/parser_impl_import_test.cc
index 6828ba76ac..ec7b869f72 100644
--- a/src/reader/spirv/parser_impl_import_test.cc
+++ b/src/reader/spirv/parser_impl_import_test.cc
@@ -114,6 +114,9 @@ TEST_F(SpvParserImportTest, Import_NonSemantic_IgnoredExtInsts) {
 )"));
   EXPECT_TRUE(p->BuildAndParseInternalModule());
   EXPECT_TRUE(p->error().empty());
+
+  p->SkipDumpingPending(
+      "crbug.com/tint/1041 track access mode in spirv-reader parser type");
 }
 
 // TODO(dneto): We don't currently support other kinds of extended instruction