diff --git a/mlir/lib/Dialect/SPIRV/Transforms/SPIRVConversion.cpp b/mlir/lib/Dialect/SPIRV/Transforms/SPIRVConversion.cpp
index cb9b7f6ec2fd2..f07307fcd2f9d 100644
--- a/mlir/lib/Dialect/SPIRV/Transforms/SPIRVConversion.cpp
+++ b/mlir/lib/Dialect/SPIRV/Transforms/SPIRVConversion.cpp
@@ -502,6 +502,11 @@ static Type convertTensorType(const spirv::TargetEnv &targetEnv,
                << type << " illegal: cannot handle zero-element tensors\n");
     return nullptr;
   }
+  if (arrayElemCount > std::numeric_limits<unsigned>::max()) {
+    LLVM_DEBUG(llvm::dbgs()
+               << type << " illegal: cannot fit tensor into target type\n");
+    return nullptr;
+  }
 
   Type arrayElemType = convertScalarType(targetEnv, options, scalarType);
   if (!arrayElemType)
diff --git a/mlir/test/Conversion/TensorToSPIRV/tensor-ops-to-spirv.mlir b/mlir/test/Conversion/TensorToSPIRV/tensor-ops-to-spirv.mlir
index b69c2d0408d17..65c6e0587129e 100644
--- a/mlir/test/Conversion/TensorToSPIRV/tensor-ops-to-spirv.mlir
+++ b/mlir/test/Conversion/TensorToSPIRV/tensor-ops-to-spirv.mlir
@@ -79,3 +79,12 @@ func.func @tensor_2d_empty() -> () {
   %x = arith.constant dense<> : tensor<2x0xi32>
   return
 }
+
+// Tensors with more than UINT32_MAX elements cannnot fit in a spirv.array.
+// Test that they are not lowered.
+// CHECK-LABEL: func @very_large_tensor
+// CHECK-NEXT:    arith.constant dense<1>
+func.func @very_large_tensor() -> () {
+  %x = arith.constant dense<1> : tensor<4294967296xi32>
+  return
+}