diff --git a/mlir/lib/Dialect/GPU/TransformOps/GPUTransformOps.cpp b/mlir/lib/Dialect/GPU/TransformOps/GPUTransformOps.cpp
--- a/mlir/lib/Dialect/GPU/TransformOps/GPUTransformOps.cpp
+++ b/mlir/lib/Dialect/GPU/TransformOps/GPUTransformOps.cpp
@@ -434,6 +434,12 @@
       rewriter.create<ThreadIdOp>(loc, indexType, Dimension::x),
       rewriter.create<ThreadIdOp>(loc, indexType, Dimension::y),
       rewriter.create<ThreadIdOp>(loc, indexType, Dimension::z)};
+  // Replace ids of dimension size 1 by zero to simplify the IR.
+  Value zero = rewriter.create<arith::ConstantIndexOp>(loc, 0);
+  for (size_t i : llvm::seq(size_t(0), globalBlockDims.size())) {
+    if (globalBlockDims[i] == 1)
+      threadOps[i] = zero;
+  }
   IRMapping bvm;
   for (auto [blockIdx, blockDim] :
        llvm::zip(foreachThreadOp.getThreadIndices(), threadMapping)) {
diff --git a/mlir/test/Dialect/GPU/transform-gpu.mlir b/mlir/test/Dialect/GPU/transform-gpu.mlir
--- a/mlir/test/Dialect/GPU/transform-gpu.mlir
+++ b/mlir/test/Dialect/GPU/transform-gpu.mlir
@@ -194,3 +194,39 @@
   %funcop = transform.structured.match ops{["gpu.launch"]} in %arg0
   transform.gpu.map_nested_foreach_to_threads %funcop { blockDim = [32]}
 }
+
+// -----
+
+!type = memref<3 x 2 x 32 x f32>
+!type1d = memref<32 x f32>
+
+// CHECK-LABEL: func.func @saxpy3d_fold_id_z(
+func.func @saxpy3d_fold_id_z(%x: !type, %y: !type, %t: !type1d, %alpha : f32, %stream : !gpu.async.token) -> !type {
+  %one = arith.constant 1 : index
+  %c12 = arith.constant 12 : index
+  %c9 = arith.constant 9 : index
+  %c7 = arith.constant 7 : index
+//  CHECK: %[[C0:.+]] = arith.constant 0 : index
+//  CHECK-NOT:   gpu.thread_id  z
+  %name = gpu.launch async[%stream] blocks(%arg3, %arg4, %arg5) in (%arg9 = %one, %arg10 = %one, %arg11 = %one)
+            threads(%arg6, %arg7, %arg8) in (%arg12 = %one, %arg13 = %one, %arg14 = %one)
+  {
+    scf.foreach_thread (%i, %j, %k) in (%one, %c7, %c9) {
+//      CHECK:   memref.load %{{.*}}[%[[C0]],
+//      CHECK:   memref.load %{{.*}}[%[[C0]],
+        %4 = memref.load %x[%i, %j, %k] : !type
+        %5 = memref.load %y[%i, %j, %k] : !type
+        %6 = math.fma %alpha, %4, %5 : f32
+//      CHECK:   memref.store %{{.*}}, %{{.*}}[%[[C0]]
+        memref.store %6, %y[%i, %j, %k] : !type
+     }  { mapping = [#gpu.thread<z>, #gpu.thread<y>, #gpu.thread<x>] }
+    gpu.terminator
+  }
+  return %y : !type
+}
+
+transform.sequence failures(propagate) {
+^bb1(%arg0: !pdl.operation):
+  %funcop = transform.structured.match ops{["gpu.launch"]} in %arg0
+  transform.gpu.map_nested_foreach_to_threads %funcop { blockDim = [12, 9, 1], syncAfterDistribute = false }
+}