diff --git a/pymc/distributions/discrete.py b/pymc/distributions/discrete.py
index d8a8c2f8fd..bb9ff075aa 100644
--- a/pymc/distributions/discrete.py
+++ b/pymc/distributions/discrete.py
@@ -1217,6 +1217,11 @@ def dist(cls, c, *args, **kwargs):
         c = at.as_tensor_variable(floatX(c))
         return super().dist([c], **kwargs)
 
+    def get_moment(rv, size, c):
+        if not rv_size_is_none(size):
+            c = at.full(size, c)
+        return c
+
     def logp(value, c):
         r"""
         Calculate log-probability of Constant distribution at specified value.
diff --git a/pymc/tests/test_distributions_moments.py b/pymc/tests/test_distributions_moments.py
index f03e1b6f9b..ae40b3bbbb 100644
--- a/pymc/tests/test_distributions_moments.py
+++ b/pymc/tests/test_distributions_moments.py
@@ -9,6 +9,7 @@
     Binomial,
     Cauchy,
     ChiSquared,
+    Constant,
     Exponential,
     Gamma,
     HalfCauchy,
@@ -382,3 +383,17 @@ def test_poisson_moment(mu, size, expected):
     with Model() as model:
         Poisson("x", mu=mu, size=size)
     assert_moment_is_expected(model, expected)
+
+
+@pytest.mark.parametrize(
+    "c, size, expected",
+    [
+        (1, None, 1),
+        (1, 5, np.full(5, 1)),
+        (np.arange(1, 6), None, np.arange(1, 6)),
+    ],
+)
+def test_constant_moment(c, size, expected):
+    with Model() as model:
+        Constant("x", c=c, size=size)
+    assert_moment_is_expected(model, expected)