diff --git a/mlir/include/mlir/IR/AffineMap.h b/mlir/include/mlir/IR/AffineMap.h
--- a/mlir/include/mlir/IR/AffineMap.h
+++ b/mlir/include/mlir/IR/AffineMap.h
@@ -327,6 +327,21 @@
 /// ```
 AffineMap concatAffineMaps(ArrayRef<AffineMap> maps);
 
+/// Returns the map that results from projecting out the dimensions specified in
+/// `projectedDimensions`. The projected dimensions are set to 0.
+///
+/// Example:
+/// 1) map                  : affine_map<(d0, d1, d2) -> (d0, d1)>
+///    projected_dimensions : {2}
+///    result               : affine_map<(d0, d1) -> (d0, d1)>
+///
+/// 2) map                  : affine_map<(d0, d1) -> (d0 + d1)>
+///    projected_dimensions : {1}
+///    result               : affine_map<(d0) -> (d0)>
+///
+/// 3) map                  : affine_map<(d0, d1, d2) -> (d0, d1)>
+///    projected_dimensions : {1}
+///    result               : affine_map<(d0, d1) -> (d0, 0)>
 AffineMap getProjectedMap(AffineMap map,
                           ArrayRef<unsigned> projectedDimensions);
 
diff --git a/mlir/lib/Dialect/Linalg/Transforms/Tiling.cpp b/mlir/lib/Dialect/Linalg/Transforms/Tiling.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/Tiling.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/Tiling.cpp
@@ -221,9 +221,8 @@
 
 static SmallVector<Value, 4>
 makeTiledShapes(OpBuilder &b, Location loc, LinalgOp linalgOp,
-                ValueRange operands, AffineMap map, ValueRange ivs,
+                ArrayRef<Value> tiledOperands, AffineMap map, ValueRange ivs,
                 ValueRange tileSizes, ValueRange allShapeSizes) {
-  assert(operands.size() == linalgOp.getShapedOperands().size());
   assert(ivs.size() == static_cast<size_t>(llvm::count_if(
                            llvm::make_range(tileSizes.begin(), tileSizes.end()),
                            [](Value v) { return !isZero(v); })) &&
@@ -243,11 +242,9 @@
     subShapeSizes.push_back(size - std_constant_index(1));
   }
 
-  auto *op = linalgOp.getOperation();
-
   SmallVector<Value, 4> res;
-  res.reserve(op->getNumOperands());
-  for (auto en : llvm::enumerate(operands)) {
+  res.reserve(tiledOperands.size());
+  for (auto en : llvm::enumerate(tiledOperands)) {
     Value shapedOp = en.value();
     ShapedType shapedType = shapedOp.getType().cast<ShapedType>();
     unsigned rank = shapedType.getRank();
@@ -342,6 +339,7 @@
   LoopIndexToRangeIndexMap loopIndexToRangeIndex;
   std::tie(loopRanges, loopIndexToRangeIndex) = makeTiledLoopRanges(
       b, op.getLoc(), shapeSizesToLoopsMap, allShapeSizes, tileSizes);
+
   SmallVector<Attribute, 4> iteratorTypes;
   for (auto attr :
        enumerate(op.iterator_types().cast<ArrayAttr>().getValue())) {
@@ -574,10 +572,10 @@
 static void insertTilingPatterns(OwningRewritePatternList &patterns,
                                  const LinalgTilingOptions &options,
                                  MLIRContext *ctx) {
-  RewritePatternList<
+  RewritePatternList<GenericOp, IndexedGenericOp,
 #define GET_OP_LIST
 #include "mlir/Dialect/Linalg/IR/LinalgStructuredOps.cpp.inc"
-      >::insert(patterns, options, ctx);
+                     >::insert(patterns, options, ctx);
 }
 
 static void applyTilingToLoopPatterns(LinalgTilingLoopType loopType,
diff --git a/mlir/test/Dialect/Linalg/tile-tensors.mlir b/mlir/test/Dialect/Linalg/tile-tensors.mlir
--- a/mlir/test/Dialect/Linalg/tile-tensors.mlir
+++ b/mlir/test/Dialect/Linalg/tile-tensors.mlir
@@ -1,4 +1,4 @@
-// RUN: mlir-opt %s -linalg-tile="linalg-tile-sizes=2,3,4" | FileCheck %s
+// RUN: mlir-opt %s -linalg-tile="linalg-tile-sizes=2,3,4" -split-input-file | FileCheck %s
 
 // CHECK-LABEL: func @matmul_tensors(
 // CHECK-SAME:    %[[TA:[0-9a-z]+]]: tensor<?x?xf32>
@@ -26,3 +26,50 @@
 //      CHECK: return %[[TD0]] : tensor<?x?xf32>
   return %0 : tensor<?x?xf32>
 }
+
+// -----
+
+func @generic_op_tensors(
+  %arg0 : tensor<?x?x?xf32>, %arg1 : tensor<?x?x?xf32>) -> tensor<?x?x?xf32> {
+  %c0 = constant 0 : index
+  %c1 = constant 1 : index
+  %c2 = constant 2 : index
+  %0 = dim %arg0, %c0 : tensor<?x?x?xf32>
+  %1 = dim %arg0, %c1 : tensor<?x?x?xf32>
+  %2 = dim %arg0, %c2 : tensor<?x?x?xf32>
+  %3 = linalg.init_tensor [%0, %1, %2] : tensor<?x?x?xf32>
+  %4 = linalg.generic
+    {indexing_maps = [affine_map<(d0, d1, d2) -> (d0, d1, d2)>,
+                      affine_map<(d0, d1, d2) -> (d0, d2, d1)>,
+		      affine_map<(d0, d1, d2) -> (d2, d1, d0)>],
+     iterator_types = ["parallel", "parallel", "parallel"]}
+    ins(%arg0, %arg1 : tensor<?x?x?xf32>, tensor<?x?x?xf32>)
+    outs(%3 : tensor<?x?x?xf32>) {
+    ^bb0(%arg2 : f32, %arg3: f32, %arg4: f32):
+      %5 = addf %arg2, %arg3 : f32
+      linalg.yield %5 : f32
+    } -> tensor<?x?x?xf32>
+  return %4 : tensor<?x?x?xf32>
+}
+
+// CHECK-LABEL: func @generic_op_tensors
+//  CHECK-SAME:   %[[ARG0:[a-zA-Z0-9_]+]]: tensor<?x?x?xf32>
+//  CHECK-SAME:   %[[ARG1:[a-zA-Z0-9_]+]]: tensor<?x?x?xf32>
+//       CHECK:   %[[INIT:.+]] = linalg.init_tensor
+//       CHECK:   %[[TD0:.+]] = scf.for %{{.+}} to %{{.+}} step %{{.+}} iter_args(%[[TC0:.+]] = %[[INIT]]) -> (tensor<?x?x?xf32>) {
+//       CHECK:     %[[TD1:.+]] = scf.for %{{.+}} to %{{.+}} step %{{.+}} iter_args(%[[TC1:.+]] = %[[TC0]]) -> (tensor<?x?x?xf32>) {
+//       CHECK:       %[[TD2:.+]] = scf.for %{{.+}} to %{{.+}} step %{{.+}} iter_args(%[[TC2:.+]] = %[[TC1]]) -> (tensor<?x?x?xf32>) {
+//       CHECK:       %[[STARG0:.+]] = subtensor %[[ARG0]][{{.+}}] : tensor<?x?x?xf32> to tensor<?x?x?xf32>
+//       CHECK:       %[[STARG1:.+]] = subtensor %[[ARG1]][{{.+}}] : tensor<?x?x?xf32> to tensor<?x?x?xf32>
+//       CHECK:       %[[STARG2:.+]] = subtensor %[[TC2]][{{.+}}] : tensor<?x?x?xf32> to tensor<?x?x?xf32>
+//       CHECK:       %[[STRETURN:.+]] = linalg.generic
+//  CHECK-SAME:         ins(%[[STARG0]], %[[STARG1]] : tensor<?x?x?xf32>, tensor<?x?x?xf32>)
+//  CHECK-SAME:         outs(%[[STARG2]] : tensor<?x?x?xf32>)
+//       CHECK:       %[[TD:.+]] = subtensor_insert %[[STRETURN]] into %[[TC2]]
+//       CHECK:       scf.yield %[[TD]]
+//       CHECK:     }
+//       CHECK:     scf.yield %[[TD2]]
+//       CHECK:   }
+//       CHECK:   scf.yield %[[TD1]]
+//       CHECK: }
+//       CHECK: return %[[TD0]]