diff --git a/mars/tensor/arithmetic/add.py b/mars/tensor/arithmetic/add.py
index 8c23399dca..327ee1cec2 100644
--- a/mars/tensor/arithmetic/add.py
+++ b/mars/tensor/arithmetic/add.py
@@ -18,6 +18,7 @@
 from functools import reduce
 
 from ... import opcodes as OperandDef
+from ...serialization.serializables import BoolField
 from ..array_utils import device, as_same_device
 from ..datasource import scalar
 from ..utils import infer_dtype
@@ -89,6 +90,8 @@ class TensorTreeAdd(TensorMultiOp):
     _op_type_ = OperandDef.TREE_ADD
     _func_name = "add"
 
+    ignore_empty_input = BoolField("ignore_empty_input", default=False)
+
     @classmethod
     def _is_sparse(cls, *args):
         if args and all(hasattr(x, "issparse") and x.issparse() for x in args):
@@ -96,10 +99,12 @@ def _is_sparse(cls, *args):
         return False
 
     @classmethod
-    def execute(cls, ctx, op):
+    def execute(cls, ctx, op: "TensorTreeAdd"):
         inputs, device_id, xp = as_same_device(
             [ctx[c.key] for c in op.inputs], device=op.device, ret_extra=True
         )
+        if op.ignore_empty_input:
+            inputs = [inp for inp in inputs if not hasattr(inp, "size") or inp.size > 0]
 
         with device(device_id):
             ctx[op.outputs[0].key] = reduce(xp.add, inputs)
diff --git a/mars/tensor/arithmetic/multiply.py b/mars/tensor/arithmetic/multiply.py
index cbc85aa36f..54bc462d9d 100644
--- a/mars/tensor/arithmetic/multiply.py
+++ b/mars/tensor/arithmetic/multiply.py
@@ -18,6 +18,7 @@
 from functools import reduce
 
 from ... import opcodes as OperandDef
+from ...serialization.serializables import BoolField
 from ..array_utils import device, as_same_device
 from ..datasource import scalar
 from ..utils import infer_dtype
@@ -88,6 +89,8 @@ class TensorTreeMultiply(TensorMultiOp):
     _op_type_ = OperandDef.TREE_MULTIPLY
     _func_name = "multiply"
 
+    ignore_empty_input = BoolField("ignore_empty_input", default=False)
+
     def __init__(self, sparse=False, **kw):
         super().__init__(sparse=sparse, **kw)
 
@@ -106,6 +109,8 @@ def execute(cls, ctx, op):
         inputs, device_id, xp = as_same_device(
             [ctx[c.key] for c in op.inputs], device=op.device, ret_extra=True
         )
+        if op.ignore_empty_input:
+            inputs = [inp for inp in inputs if not hasattr(inp, "size") or inp.size > 0]
 
         with device(device_id):
             ctx[op.outputs[0].key] = reduce(xp.multiply, inputs)
diff --git a/mars/tensor/reduction/core.py b/mars/tensor/reduction/core.py
index a3f6824a26..2ecd335dbb 100644
--- a/mars/tensor/reduction/core.py
+++ b/mars/tensor/reduction/core.py
@@ -586,7 +586,11 @@ def tile(cls, op):
                 to_cum_chunks.append(sliced_chunk)
             to_cum_chunks.append(chunk)
 
-            bin_op = bin_op_type(args=to_cum_chunks, dtype=chunk.dtype)
+            # GH#3132: some chunks of to_cum_chunks may be empty,
+            # so we tell tree_add&tree_multiply to ignore them
+            bin_op = bin_op_type(
+                args=to_cum_chunks, dtype=chunk.dtype, ignore_empty_input=True
+            )
             output_chunk = bin_op.new_chunk(
                 to_cum_chunks,
                 shape=chunk.shape,
diff --git a/mars/tensor/reduction/tests/test_reduction_execution.py b/mars/tensor/reduction/tests/test_reduction_execution.py
index 340d5c551f..0059092e69 100644
--- a/mars/tensor/reduction/tests/test_reduction_execution.py
+++ b/mars/tensor/reduction/tests/test_reduction_execution.py
@@ -497,6 +497,16 @@ def test_cum_reduction(setup):
         np.cumsum(np.array(list("abcdefghi"), dtype=object)),
     )
 
+    # test empty chunks
+    raw = np.random.rand(100)
+    arr = tensor(raw, chunk_size=((0, 100),))
+    res = arr.cumsum().execute().fetch()
+    expected = raw.cumsum()
+    np.testing.assert_allclose(res, expected)
+    res = arr.cumprod().execute().fetch()
+    expected = raw.cumprod()
+    np.testing.assert_allclose(res, expected)
+
 
 def test_nan_cum_reduction(setup):
     raw = np.random.randint(5, size=(8, 8, 8)).astype(float)
diff --git a/mars/tensor/reshape/reshape.py b/mars/tensor/reshape/reshape.py
index edee28d5e8..a921fc65f6 100644
--- a/mars/tensor/reshape/reshape.py
+++ b/mars/tensor/reshape/reshape.py
@@ -603,7 +603,9 @@ def reshape(a, newshape, order="C"):
 
     tensor_order = get_order(order, a.order, available_options="CFA")
 
-    if a.shape == newshape and tensor_order == a.order:
+    if a.shape == newshape and (
+        a.ndim <= 1 or (a.ndim > 1 and tensor_order == a.order)
+    ):
         # does not need to reshape
         return a
     return _reshape(