diff --git a/mlir/lib/Transforms/BufferPlacement.cpp b/mlir/lib/Transforms/BufferPlacement.cpp
--- a/mlir/lib/Transforms/BufferPlacement.cpp
+++ b/mlir/lib/Transforms/BufferPlacement.cpp
@@ -700,15 +700,19 @@
 BufferAssignmentTypeConverter::BufferAssignmentTypeConverter() {
   // Keep all types unchanged.
   addConversion([](Type type) { return type; });
-  // A type conversion that converts ranked-tensor type to memref type.
+  // Convert RankedTensorType to MemRefType.
   addConversion([](RankedTensorType type) {
     return (Type)MemRefType::get(type.getShape(), type.getElementType());
   });
+  // Convert UnrankedTensorType to UnrankedMemRefType.
+  addConversion([](UnrankedTensorType type) {
+    return (Type)UnrankedMemRefType::get(type.getElementType(), 0);
+  });
 }
 
 /// Checks if `type` has been converted from non-memref type to memref.
 bool BufferAssignmentTypeConverter::isConvertedMemref(Type type, Type before) {
-  return type.isa<MemRefType>() && !before.isa<MemRefType>();
+  return type.isa<BaseMemRefType>() && !before.isa<BaseMemRefType>();
 }
 
 //===----------------------------------------------------------------------===//
diff --git a/mlir/test/Transforms/buffer-placement-preparation-allowed-memref-results.mlir b/mlir/test/Transforms/buffer-placement-preparation-allowed-memref-results.mlir
--- a/mlir/test/Transforms/buffer-placement-preparation-allowed-memref-results.mlir
+++ b/mlir/test/Transforms/buffer-placement-preparation-allowed-memref-results.mlir
@@ -64,6 +64,15 @@
 
 // -----
 
+// CHECK-LABEL: func @func_with_unranked_arg_and_result
+func @func_with_unranked_arg_and_result(%arg0: tensor<*xf32>) -> tensor<*xf32> {
+  return %arg0 : tensor<*xf32>
+}
+// CHECK-SAME: ([[ARG:%.*]]: memref<*xf32>) -> memref<*xf32>
+// CHECK-NEXT: return [[ARG]] : memref<*xf32>
+
+// -----
+
 // CHECK-LABEL: func @func_and_block_signature_conversion
 func @func_and_block_signature_conversion(%arg0 : tensor<2xf32>, %cond : i1, %arg1: tensor<4x4xf32>) -> tensor<4x4xf32>{
     cond_br %cond, ^bb1, ^bb2
diff --git a/mlir/test/Transforms/buffer-placement-preparation.mlir b/mlir/test/Transforms/buffer-placement-preparation.mlir
--- a/mlir/test/Transforms/buffer-placement-preparation.mlir
+++ b/mlir/test/Transforms/buffer-placement-preparation.mlir
@@ -284,3 +284,9 @@
 // CHECK: %[[Y1:.*]] = call @callee(%[[X0]], %[[Y0]])
 // CHECK: linalg.copy(%[[Y0]], %[[CALLER_RESULT]])
 // CHECK: return
+
+// CHECK-LABEL: func @func_with_unranked_arg
+func @func_with_unranked_arg(%arg0: tensor<*xf32>) {
+  return
+}
+// CHECK-SAME: ([[ARG:%.*]]: memref<*xf32>)