diff --git a/tensorflow/core/kernels/reduction_ops_common.cc b/tensorflow/core/kernels/reduction_ops_common.cc
index 8818f7befb6..5511b8f43cc 100644
--- a/tensorflow/core/kernels/reduction_ops_common.cc
+++ b/tensorflow/core/kernels/reduction_ops_common.cc
@@ -61,12 +61,13 @@ Status ReductionHelper::Simplify(const Tensor& data, const Tensor& axis,
   gtl::InlinedVector<bool, 4> bitmap(data.dims(), false);
   auto axis_vec = axis.flat<int32>();
   for (int64 i = 0; i < axis.NumElements(); ++i) {
-    const int32 index = axis_vec(i);
-    if (index < 0 || index >= data.dims()) {
+    int32 index = axis_vec(i);
+    if (index < -data.dims() || index >= data.dims()) {
       return errors::InvalidArgument("Invalid reduction dimension (", index,
                                      " for input with ", data.dims(),
                                      " dimension(s)");
     }
+    index = (index + data.dims()) % data.dims();
     bitmap[index] = true;
   }
 
diff --git a/tensorflow/python/kernel_tests/reduction_ops_test.py b/tensorflow/python/kernel_tests/reduction_ops_test.py
index d330040db4d..e9d21fe1a40 100644
--- a/tensorflow/python/kernel_tests/reduction_ops_test.py
+++ b/tensorflow/python/kernel_tests/reduction_ops_test.py
@@ -27,34 +27,40 @@ from tensorflow.python.ops import math_ops
 
 class ReducedShapeTest(tf.test.TestCase):
 
+  def _check(self, shape, axes, result):
+    output = math_ops.reduced_shape(shape, axes=axes)
+    self.assertAllEqual(output.eval(), result)
+
   def testSimple(self):
     with self.test_session():
-      def check(shape, axes, result):
-        output = math_ops.reduced_shape(shape, axes=axes)
-        self.assertAllEqual(output.eval(), result)
-      check([3], [], [3])
-      check([3], [0], [1])
-      check([5, 3], [], [5, 3])
-      check([5, 3], [0], [1, 3])
-      check([5, 3], [1], [5, 1])
-      check([5, 3], [0, 1], [1, 1])
+      self._check([3], [], [3])
+      self._check([3], [0], [1])
+      self._check([5, 3], [], [5, 3])
+      self._check([5, 3], [0], [1, 3])
+      self._check([5, 3], [1], [5, 1])
+      self._check([5, 3], [0, 1], [1, 1])
 
   def testZeros(self):
     """Check that reduced_shape does the right thing with zero dimensions."""
     with self.test_session():
-      def check(shape, axes, result):
-        output = math_ops.reduced_shape(shape, axes=axes)
-        self.assertAllEqual(output.eval(), result)
-      check([0], [], [0])
-      check([0], [0], [1])
-      check([0, 3], [], [0, 3])
-      check([0, 3], [0], [1, 3])
-      check([0, 3], [1], [0, 1])
-      check([0, 3], [0, 1], [1, 1])
-      check([3, 0], [], [3, 0])
-      check([3, 0], [0], [1, 0])
-      check([3, 0], [1], [3, 1])
-      check([3, 0], [0, 1], [1, 1])
+      self._check([0], [], [0])
+      self._check([0], [0], [1])
+      self._check([0, 3], [], [0, 3])
+      self._check([0, 3], [0], [1, 3])
+      self._check([0, 3], [1], [0, 1])
+      self._check([0, 3], [0, 1], [1, 1])
+      self._check([3, 0], [], [3, 0])
+      self._check([3, 0], [0], [1, 0])
+      self._check([3, 0], [1], [3, 1])
+      self._check([3, 0], [0, 1], [1, 1])
+
+  def testNegAxes(self):
+    with self.test_session():
+      self._check([10, 10, 10], [-1], [10, 10, 1])
+      self._check([10, 10, 10], [-1, 2], [10, 10, 1])
+      self._check([10, 10, 10], [-1, -1], [10, 10, 1])
+      self._check([10, 10, 10], [-1, 0], [1, 10, 1])
+      self._check([10, 10, 10], [-3], [1, 10, 10])
 
 
 class SumReductionTest(tf.test.TestCase):
@@ -110,6 +116,9 @@ class SumReductionTest(tf.test.TestCase):
     self._compareAll(np_arr, [1, 2])
     self._compareAll(np_arr, [0, 2])
     self._compareAll(np_arr, [0, 1, 2])
+    self._compareAll(np_arr, [-1])
+    self._compareAll(np_arr, [-1, -3])
+    self._compareAll(np_arr, [-1, 1])
 
   def testFloatReduce4D(self):
     # Create a 4D array of floats and reduce across some
@@ -167,7 +176,7 @@ class SumReductionTest(tf.test.TestCase):
     input_tensor = tf.convert_to_tensor(np_arr)
     with self.assertRaisesWithPredicateMatch(
         ValueError, lambda e: "Invalid reduction dimension" in str(e)):
-      tf.reduce_sum(input_tensor, [-1])
+      tf.reduce_sum(input_tensor, [-3])
     with self.assertRaisesWithPredicateMatch(
         ValueError, lambda e: "Invalid reduction dimension" in str(e)):
       tf.reduce_sum(input_tensor, [2])
diff --git a/tensorflow/python/ops/math_ops.py b/tensorflow/python/ops/math_ops.py
index adb673f8510..c622d834906 100644
--- a/tensorflow/python/ops/math_ops.py
+++ b/tensorflow/python/ops/math_ops.py
@@ -1527,10 +1527,14 @@ def _ReductionShape(op):
   reduction_indices = np.ravel(reduction_indices)
 
   for reduction_index in reduction_indices:
-    if reduction_index < 0 or reduction_index >= input_shape.ndims:
+    if (reduction_index < -input_shape.ndims or
+        reduction_index >= input_shape.ndims):
       raise ValueError("Invalid reduction dimension %d for input with %d "
                        "dimensions" % (reduction_index, input_shape.ndims))
 
+  reduction_indices = set([(x + input_shape.ndims) % input_shape.ndims
+                           for x in reduction_indices])
+
   returned_dims = []
   if keep_dims:
     for i, dim in enumerate(input_shape.dims):
@@ -1624,6 +1628,7 @@ def reduced_shape(input_shape, axes):
   axes = to_int32(axes)                     # [1, 2]
 
   input_rank = array_ops.size(input_shape)  # 4
+  axes = (axes + input_rank) % input_rank
   axes_shape = array_ops.shape(axes)        # [2]
   return gen_data_flow_ops.dynamic_stitch(  # [2, 1, 1, 7]
       [range(input_rank),                   # [0, 1, 2, 3]