diff --git a/python/paddle/fluid/tests/unittests/test_case.py b/python/paddle/fluid/tests/unittests/test_case.py
index 9123b4b009d1866d7ce9385777e4ddc5ffc0d5e0..675b51cf0a0535e0cc34f900477e3e2aaf8ee76a 100644
--- a/python/paddle/fluid/tests/unittests/test_case.py
+++ b/python/paddle/fluid/tests/unittests/test_case.py
@@ -22,6 +22,7 @@ import paddle.fluid as fluid
 import paddle.fluid.core as core
 import paddle.fluid.layers as layers
 import paddle.fluid.optimizer as optimizer
+from paddle.fluid.backward import append_backward
 from paddle.fluid.framework import Program, program_guard
 
 paddle.enable_static()
@@ -145,10 +146,101 @@ class TestAPICase(unittest.TestCase):
             )
 
             np.testing.assert_allclose(res[0], 1, rtol=1e-05)
+            self.assertEqual(res[0].shape, ())
             np.testing.assert_allclose(res[1], 2, rtol=1e-05)
+            self.assertEqual(res[1].shape, ())
             np.testing.assert_allclose(res[2], 3, rtol=1e-05)
+            self.assertEqual(res[2].shape, ())
             np.testing.assert_allclose(res[3], 2, rtol=1e-05)
+            self.assertEqual(res[3].shape, ())
             np.testing.assert_allclose(res[4], 2, rtol=1e-05)
+            self.assertEqual(res[4].shape, ())
+
+    def test_0d_tensor_backward(self):
+        main_program = Program()
+        startup_program = Program()
+        with program_guard(main_program, startup_program):
+            x = paddle.full(shape=[], dtype='float32', fill_value=-2.0)
+            x.stop_gradient = False
+            pred = paddle.full(shape=[], dtype='bool', fill_value=0)
+            # pred is False, so out = -x
+            out = paddle.static.nn.case(
+                pred_fn_pairs=[(pred, lambda: x)], default=lambda: -x
+            )
+            append_backward(out)
+
+        place = (
+            fluid.CUDAPlace(0)
+            if core.is_compiled_with_cuda()
+            else fluid.CPUPlace()
+        )
+        exe = fluid.Executor(place)
+
+        res = exe.run(main_program, fetch_list=[out.name, x.grad_name])
+        np.testing.assert_allclose(
+            np.asarray(res[0]), np.array(2.0), rtol=1e-05
+        )
+        self.assertEqual(res[0].shape, ())
+        np.testing.assert_allclose(
+            np.asarray(res[1]), np.array(-1.0), rtol=1e-05
+        )
+        self.assertEqual(res[1].shape, ())
+
+    def test_0d_tensor_dygraph(self):
+        paddle.disable_static()
+
+        def fn_1():
+            return paddle.full(shape=[], dtype='int32', fill_value=1)
+
+        def fn_2():
+            return paddle.full(shape=[], dtype='int32', fill_value=2)
+
+        def fn_3():
+            return paddle.full(shape=[], dtype='int32', fill_value=3)
+
+        x = paddle.full(shape=[], dtype='float32', fill_value=0.3)
+        y = paddle.full(shape=[], dtype='float32', fill_value=0.1)
+        z = paddle.full(shape=[], dtype='float32', fill_value=0.2)
+        pred_2 = paddle.less_than(x, y)  # false: 0.3 < 0.1
+        pred_1 = paddle.less_than(z, x)  # true: 0.2 < 0.3
+
+        # call fn_1
+        out_0 = paddle.static.nn.control_flow.case(
+            pred_fn_pairs=[(pred_1, fn_1), (pred_1, fn_2)], default=fn_3
+        )
+
+        # call fn_2
+        out_1 = paddle.static.nn.control_flow.case(
+            pred_fn_pairs=[(pred_2, fn_1), (pred_1, fn_2)], default=fn_3
+        )
+
+        # call default fn_3
+        out_2 = paddle.static.nn.control_flow.case(
+            pred_fn_pairs=((pred_2, fn_1), (pred_2, fn_2)), default=fn_3
+        )
+
+        # no default, call fn_2
+        out_3 = paddle.static.nn.control_flow.case(
+            pred_fn_pairs=[(pred_1, fn_2)]
+        )
+
+        # no default, call fn_2. but pred_2 is false
+        out_4 = paddle.static.nn.control_flow.case(
+            pred_fn_pairs=[(pred_2, fn_2)]
+        )
+
+        np.testing.assert_allclose(out_0, 1, rtol=1e-05)
+        self.assertEqual(out_0.shape, [])
+        np.testing.assert_allclose(out_1, 2, rtol=1e-05)
+        self.assertEqual(out_1.shape, [])
+        np.testing.assert_allclose(out_2, 3, rtol=1e-05)
+        self.assertEqual(out_2.shape, [])
+        np.testing.assert_allclose(out_3, 2, rtol=1e-05)
+        self.assertEqual(out_3.shape, [])
+        np.testing.assert_allclose(out_4, 2, rtol=1e-05)
+        self.assertEqual(out_4.shape, [])
+
+        paddle.enable_static()
 
     def test_return_var_tuple(self):
         def fn_1():
@@ -394,8 +486,11 @@ class TestAPICase_Nested(unittest.TestCase):
             res = exe.run(main_program, fetch_list=[out_1, out_2, out_3])
 
             np.testing.assert_allclose(res[0], 1, rtol=1e-05)
+            self.assertEqual(res[0].shape, ())
             np.testing.assert_allclose(res[1], 2, rtol=1e-05)
+            self.assertEqual(res[1].shape, ())
             np.testing.assert_allclose(res[2], 3, rtol=1e-05)
+            self.assertEqual(res[2].shape, ())
 
 
 class TestAPICase_Error(unittest.TestCase):
diff --git a/python/paddle/fluid/tests/unittests/test_switch_case.py b/python/paddle/fluid/tests/unittests/test_switch_case.py
index 2ddbd0f7ff051e246d3e6e3bb54cc2bddab25e4a..3fad3bdfd0c0db108fe20764d28d59766a91755c 100644
--- a/python/paddle/fluid/tests/unittests/test_switch_case.py
+++ b/python/paddle/fluid/tests/unittests/test_switch_case.py
@@ -21,6 +21,7 @@ import paddle
 import paddle.fluid as fluid
 import paddle.fluid.core as core
 import paddle.fluid.layers as layers
+from paddle.fluid.backward import append_backward
 from paddle.fluid.framework import Program, program_guard
 
 paddle.enable_static()
@@ -93,25 +94,25 @@ class TestAPISwitchCase(unittest.TestCase):
                 res[1],
                 2,
                 rtol=1e-05,
-                err_msg='result is {} but answer is {}'.format(res[0], 2),
+                err_msg='result is {} but answer is {}'.format(res[1], 2),
             )
             np.testing.assert_allclose(
                 res[2],
                 3,
                 rtol=1e-05,
-                err_msg='result is {} but answer is {}'.format(res[0], 3),
+                err_msg='result is {} but answer is {}'.format(res[2], 3),
             )
             np.testing.assert_allclose(
                 res[3],
                 2,
                 rtol=1e-05,
-                err_msg='result is {} but answer is {}'.format(res[0], 2),
+                err_msg='result is {} but answer is {}'.format(res[3], 2),
             )
             np.testing.assert_allclose(
                 res[4],
                 2,
                 rtol=1e-05,
-                err_msg='result is {} but answer is {}'.format(res[0], 2),
+                err_msg='result is {} but answer is {}'.format(res[4], 2),
             )
 
     def test_0d_tensor(self):
@@ -176,30 +177,148 @@ class TestAPISwitchCase(unittest.TestCase):
                 rtol=1e-05,
                 err_msg='result is {} but answer is {}'.format(res[0], 1),
             )
+            self.assertEqual(res[0].shape, ())
             np.testing.assert_allclose(
                 res[1],
                 2,
                 rtol=1e-05,
-                err_msg='result is {} but answer is {}'.format(res[0], 2),
+                err_msg='result is {} but answer is {}'.format(res[1], 2),
             )
+            self.assertEqual(res[1].shape, ())
             np.testing.assert_allclose(
                 res[2],
                 3,
                 rtol=1e-05,
-                err_msg='result is {} but answer is {}'.format(res[0], 3),
+                err_msg='result is {} but answer is {}'.format(res[2], 3),
             )
+            self.assertEqual(res[2].shape, ())
             np.testing.assert_allclose(
                 res[3],
                 2,
                 rtol=1e-05,
-                err_msg='result is {} but answer is {}'.format(res[0], 2),
+                err_msg='result is {} but answer is {}'.format(res[3], 2),
             )
+            self.assertEqual(res[3].shape, ())
             np.testing.assert_allclose(
                 res[4],
                 2,
                 rtol=1e-05,
-                err_msg='result is {} but answer is {}'.format(res[0], 2),
+                err_msg='result is {} but answer is {}'.format(res[4], 2),
             )
+            self.assertEqual(res[4].shape, ())
+
+    def test_0d_tensor_backward(self):
+        main_program = Program()
+        startup_program = Program()
+        with program_guard(main_program, startup_program):
+            x = paddle.full(shape=[], dtype='float32', fill_value=-2.0)
+            x.stop_gradient = False
+            pred = paddle.full(shape=[], dtype='int32', fill_value=2)
+            # pred is 2, so out = 2 * x
+            out = paddle.static.nn.switch_case(
+                branch_index=pred,
+                branch_fns=[(1, lambda: x), (2, lambda: 2 * x)],
+                default=lambda: -x,
+            )
+            append_backward(out)
+
+        place = (
+            fluid.CUDAPlace(0)
+            if core.is_compiled_with_cuda()
+            else fluid.CPUPlace()
+        )
+        exe = fluid.Executor(place)
+
+        res = exe.run(main_program, fetch_list=[out.name, x.grad_name])
+        np.testing.assert_allclose(
+            np.asarray(res[0]), np.array(-4.0), rtol=1e-05
+        )
+        self.assertEqual(res[0].shape, ())
+        np.testing.assert_allclose(
+            np.asarray(res[1]), np.array(2.0), rtol=1e-05
+        )
+        self.assertEqual(res[1].shape, ())
+
+    def test_0d_tensor_dygraph(self):
+        paddle.disable_static()
+
+        def fn_1():
+            return paddle.full(shape=[], dtype='int32', fill_value=1)
+
+        def fn_2():
+            return paddle.full(shape=[], dtype='int32', fill_value=2)
+
+        def fn_3():
+            return paddle.full(shape=[], dtype='int32', fill_value=3)
+
+        index_1 = paddle.full(shape=[], dtype='int32', fill_value=1)
+        index_2 = paddle.full(shape=[], dtype='int32', fill_value=2)
+        index_5 = paddle.full(shape=[], dtype='int32', fill_value=5)
+
+        # call fn_1
+        out_0 = paddle.static.nn.switch_case(
+            branch_index=index_1, branch_fns={1: fn_1, 2: fn_2, 3: fn_3}
+        )
+
+        # call fn_2 : branch_fns={0: fn_1, 1:fn_2, 2:fn_3}
+        out_1 = paddle.static.nn.switch_case(
+            branch_index=index_1, branch_fns=(fn_1, fn_2, fn_3)
+        )
+
+        # call default fn_3
+        out_2 = paddle.static.nn.switch_case(
+            branch_index=index_5,
+            branch_fns=((1, fn_1), (2, fn_2)),
+            default=fn_3,
+        )
+
+        # no default, call fn_2
+        out_3 = paddle.static.nn.switch_case(
+            branch_index=index_2, branch_fns=[(1, fn_1), (2, fn_2)]
+        )
+
+        # no default, call fn_2 but branch_index is 5
+        out_4 = paddle.static.nn.switch_case(
+            branch_index=index_5,
+            branch_fns=[(1, fn_1), (3, fn_2), (2, fn_3)],
+        )
+        np.testing.assert_allclose(
+            out_0,
+            1,
+            rtol=1e-05,
+            err_msg='result is {} but answer is {}'.format(out_0, 1),
+        )
+        self.assertEqual(out_0.shape, [])
+        np.testing.assert_allclose(
+            out_1,
+            2,
+            rtol=1e-05,
+            err_msg='result is {} but answer is {}'.format(out_1, 2),
+        )
+        self.assertEqual(out_1.shape, [])
+        np.testing.assert_allclose(
+            out_2,
+            3,
+            rtol=1e-05,
+            err_msg='result is {} but answer is {}'.format(out_2, 3),
+        )
+        self.assertEqual(out_2.shape, [])
+        np.testing.assert_allclose(
+            out_3,
+            2,
+            rtol=1e-05,
+            err_msg='result is {} but answer is {}'.format(out_3, 2),
+        )
+        self.assertEqual(out_3.shape, [])
+        np.testing.assert_allclose(
+            out_4,
+            2,
+            rtol=1e-05,
+            err_msg='result is {} but answer is {}'.format(out_4, 2),
+        )
+        self.assertEqual(out_4.shape, [])
+
+        paddle.enable_static()
 
     def test_return_var_tuple(self):
         def fn_1():
@@ -426,18 +545,21 @@ class TestAPISwitchCase_Nested(unittest.TestCase):
                 rtol=1e-05,
                 err_msg='result is {} but answer is {}'.format(res[0], 1),
             )
+            self.assertEqual(res[0].shape, ())
             np.testing.assert_allclose(
                 res[1],
                 2,
                 rtol=1e-05,
                 err_msg='result is {} but answer is {}'.format(res[1], 2),
             )
+            self.assertEqual(res[1].shape, ())
             np.testing.assert_allclose(
                 res[2],
                 3,
                 rtol=1e-05,
                 err_msg='result is {} but answer is {}'.format(res[2], 3),
             )
+            self.assertEqual(res[2].shape, ())
 
 
 # test TypeError and ValueError of api switch_case