diff --git a/pymc3/distributions/continuous.py b/pymc3/distributions/continuous.py
index 6b05961191..43ae2f29b4 100644
--- a/pymc3/distributions/continuous.py
+++ b/pymc3/distributions/continuous.py
@@ -571,15 +571,17 @@ def __init__(self, mu=0, sigma=None, tau=None, lower=None, upper=None,
         tau, sigma = get_tau_sigma(tau=tau, sigma=sigma)
         self.sigma = self.sd = tt.as_tensor_variable(sigma)
         self.tau = tt.as_tensor_variable(tau)
-        self.lower = tt.as_tensor_variable(floatX(lower)) if lower is not None else lower
-        self.upper = tt.as_tensor_variable(floatX(upper)) if upper is not None else upper
+        self.lower_check = tt.as_tensor_variable(floatX(lower)) if lower is not None else lower
+        self.upper_check = tt.as_tensor_variable(floatX(upper)) if upper is not None else upper
+        self.lower = tt.as_tensor_variable(floatX(lower)) if lower is not None else tt.as_tensor_variable(floatX(-np.inf))
+        self.upper = tt.as_tensor_variable(floatX(upper)) if upper is not None else tt.as_tensor_variable(floatX(np.inf))
         self.mu = tt.as_tensor_variable(floatX(mu))
 
-        if self.lower is None and self.upper is None:
+        if self.lower_check is None and self.upper_check is None:
             self._defaultval = mu
-        elif self.lower is None and self.upper is not None:
+        elif self.lower_check is None and self.upper_check is not None:
             self._defaultval = self.upper - 1.
-        elif self.lower is not None and self.upper is None:
+        elif self.lower_check is not None and self.upper_check is None:
             self._defaultval = self.lower + 1.
         else:
             self._defaultval = (self.lower + self.upper) / 2
@@ -639,19 +641,19 @@ def logp(self, value):
         logp = Normal.dist(mu=mu, sigma=sigma).logp(value) - norm
 
         bounds = [sigma > 0]
-        if self.lower is not None:
+        if self.lower_check is not None:
             bounds.append(value >= self.lower)
-        if self.upper is not None:
+        if self.upper_check is not None:
             bounds.append(value <= self.upper)
         return bound(logp, *bounds)
 
     def _normalization(self):
         mu, sigma = self.mu, self.sigma
 
-        if self.lower is None and self.upper is None:
+        if self.lower_check is None and self.upper_check is None:
             return 0.
 
-        if self.lower is not None and self.upper is not None:
+        if self.lower_check is not None and self.upper_check is not None:
             lcdf_a = normal_lcdf(mu, sigma, self.lower)
             lcdf_b = normal_lcdf(mu, sigma, self.upper)
             lsf_a = normal_lccdf(mu, sigma, self.lower)
@@ -663,7 +665,7 @@ def _normalization(self):
                 logdiffexp(lcdf_b, lcdf_a),
             )
 
-        if self.lower is not None:
+        if self.lower_check is not None:
             return normal_lccdf(mu, sigma, self.lower)
         else:
             return normal_lcdf(mu, sigma, self.upper)
diff --git a/pymc3/tests/test_distributions_random.py b/pymc3/tests/test_distributions_random.py
index 6fa49ca843..55ce66bce9 100644
--- a/pymc3/tests/test_distributions_random.py
+++ b/pymc3/tests/test_distributions_random.py
@@ -259,6 +259,14 @@ class TestTruncatedNormal(BaseTestCases.BaseTestCase):
     distribution = pm.TruncatedNormal
     params = {'mu': 0., 'tau': 1., 'lower':-0.5, 'upper':0.5}
 
+class TestTruncatedNormalLower(BaseTestCases.BaseTestCase):
+    distribution = pm.TruncatedNormal
+    params = {'mu': 0., 'tau': 1., 'lower':-0.5}
+
+class TestTruncatedNormalUpper(BaseTestCases.BaseTestCase):
+    distribution = pm.TruncatedNormal
+    params = {'mu': 0., 'tau': 1., 'upper':0.5}
+
 class TestSkewNormal(BaseTestCases.BaseTestCase):
     distribution = pm.SkewNormal
     params = {'mu': 0., 'sigma': 1., 'alpha': 5.}
@@ -475,6 +483,18 @@ def ref_rand(size, mu, sigma, lower, upper):
         pymc3_random(pm.TruncatedNormal, {'mu': R, 'sigma': Rplusbig, 'lower':-Rplusbig, 'upper':Rplusbig},
                      ref_rand=ref_rand)
 
+    def test_truncated_normal_lower(self):
+        def ref_rand(size, mu, sigma, lower):
+            return st.truncnorm.rvs((lower-mu)/sigma, np.inf, size=size, loc=mu, scale=sigma)
+        pymc3_random(pm.TruncatedNormal, {'mu': R, 'sigma': Rplusbig, 'lower':-Rplusbig},
+                     ref_rand=ref_rand)
+
+    def test_truncated_normal_upper(self):
+        def ref_rand(size, mu, sigma, upper):
+            return st.truncnorm.rvs(-np.inf, (upper-mu)/sigma, size=size, loc=mu, scale=sigma)
+        pymc3_random(pm.TruncatedNormal, {'mu': R, 'sigma': Rplusbig, 'upper':Rplusbig},
+                     ref_rand=ref_rand)
+
     def test_skew_normal(self):
         def ref_rand(size, alpha, mu, sigma):
             return st.skewnorm.rvs(size=size, a=alpha, loc=mu, scale=sigma)