diff --git a/RELEASE-NOTES.md b/RELEASE-NOTES.md
index fc85b4a86db..b260a82e17d 100644
--- a/RELEASE-NOTES.md
+++ b/RELEASE-NOTES.md
@@ -14,6 +14,7 @@
 - `ScalarSharedVariable` can now be used as an input to other RVs directly (see [#4445](https://github.com/pymc-devs/pymc3/pull/4445)).
 - `pm.sample` and `pm.find_MAP` no longer change the `start` argument (see [#4458](https://github.com/pymc-devs/pymc3/pull/4458)).
 - Fixed `Dirichlet.logp` method to work with unit batch or event shapes (see [#4454](https://github.com/pymc-devs/pymc3/pull/4454)).
+- Bugfix in logp and logcdf methods of `Triangular` distribution (see[#4470](https://github.com/pymc-devs/pymc3/pull/4470)).
 
 ## PyMC3 3.11.0 (21 January 2021)
 
diff --git a/pymc3/distributions/continuous.py b/pymc3/distributions/continuous.py
index 5c990bde3b5..234ed935f2b 100644
--- a/pymc3/distributions/continuous.py
+++ b/pymc3/distributions/continuous.py
@@ -29,7 +29,6 @@
 from pymc3.distributions import transforms
 from pymc3.distributions.dist_math import (
     SplineWrapper,
-    alltrue_elemwise,
     betaln,
     bound,
     clipped_beta_rvs,
@@ -3649,18 +3648,14 @@ def logp(self, value):
         c = self.c
         lower = self.lower
         upper = self.upper
-        return tt.switch(
-            alltrue_elemwise([lower <= value, value < c]),
-            tt.log(2 * (value - lower) / ((upper - lower) * (c - lower))),
+        return bound(
             tt.switch(
-                tt.eq(value, c),
-                tt.log(2 / (upper - lower)),
-                tt.switch(
-                    alltrue_elemwise([c < value, value <= upper]),
-                    tt.log(2 * (upper - value) / ((upper - lower) * (upper - c))),
-                    np.inf,
-                ),
+                tt.lt(value, c),
+                tt.log(2 * (value - lower) / ((upper - lower) * (c - lower))),
+                tt.log(2 * (upper - value) / ((upper - lower) * (upper - c))),
             ),
+            lower <= value,
+            value <= upper,
         )
 
     def logcdf(self, value):
@@ -3678,17 +3673,24 @@ def logcdf(self, value):
         -------
         TensorVariable
         """
-        l = self.lower
-        u = self.upper
         c = self.c
-        return tt.switch(
-            tt.le(value, l),
-            -np.inf,
+        lower = self.lower
+        upper = self.upper
+        return bound(
             tt.switch(
-                tt.le(value, c),
-                tt.log(((value - l) ** 2) / ((u - l) * (c - l))),
-                tt.switch(tt.lt(value, u), tt.log1p(-((u - value) ** 2) / ((u - l) * (u - c))), 0),
+                tt.le(value, lower),
+                -np.inf,
+                tt.switch(
+                    tt.le(value, c),
+                    tt.log(((value - lower) ** 2) / ((upper - lower) * (c - lower))),
+                    tt.switch(
+                        tt.lt(value, upper),
+                        tt.log1p(-((upper - value) ** 2) / ((upper - lower) * (upper - c))),
+                        0,
+                    ),
+                ),
             ),
+            lower <= upper,
         )
 
 
diff --git a/pymc3/tests/test_distributions.py b/pymc3/tests/test_distributions.py
index 2f9c9672aef..06efc90b8d8 100644
--- a/pymc3/tests/test_distributions.py
+++ b/pymc3/tests/test_distributions.py
@@ -802,6 +802,10 @@ def test_uniform(self):
             lambda value, lower, upper: sp.uniform.logcdf(value, lower, upper - lower),
             skip_paramdomain_outside_edge_test=True,
         )
+        # Custom logp / logcdf check for invalid parameters
+        invalid_dist = Uniform.dist(lower=1, upper=0)
+        assert invalid_dist.logp(0.5).tag.test_value == -np.inf
+        assert invalid_dist.logcdf(2).tag.test_value == -np.inf
 
     def test_triangular(self):
         self.check_logp(
@@ -817,6 +821,14 @@ def test_triangular(self):
             lambda value, c, lower, upper: sp.triang.logcdf(value, c - lower, lower, upper - lower),
             skip_paramdomain_outside_edge_test=True,
         )
+        # Custom logp check for invalid value
+        valid_dist = Triangular.dist(lower=0, upper=1, c=2.0)
+        assert np.all(valid_dist.logp(np.array([1.9, 2.0, 2.1])).tag.test_value == -np.inf)
+
+        # Custom logp / logcdf check for invalid parameters
+        invalid_dist = Triangular.dist(lower=1, upper=0, c=2.0)
+        assert invalid_dist.logp(0.5).tag.test_value == -np.inf
+        assert invalid_dist.logcdf(2).tag.test_value == -np.inf
 
     def test_bound_normal(self):
         PositiveNormal = Bound(Normal, lower=0.0)
@@ -850,6 +862,10 @@ def test_discrete_unif(self):
             Rdunif,
             {"lower": -Rplusdunif, "upper": Rplusdunif},
         )
+        # Custom logp / logcdf check for invalid parameters
+        invalid_dist = DiscreteUniform.dist(lower=1, upper=0)
+        assert invalid_dist.logp(0.5).tag.test_value == -np.inf
+        assert invalid_dist.logcdf(2).tag.test_value == -np.inf
 
     def test_flat(self):
         self.check_logp(Flat, Runif, {}, lambda value: 0)