diff --git a/pymc/distributions/truncated.py b/pymc/distributions/truncated.py
index 05616fbe4c..f44de3c018 100644
--- a/pymc/distributions/truncated.py
+++ b/pymc/distributions/truncated.py
@@ -352,6 +352,50 @@ def truncated_logprob(op, values, *inputs, **kwargs):
     return logp
 
 
+@_logcdf.register(TruncatedRV)
+def truncated_logcdf(op, value, *inputs, **kwargs):
+    *rv_inputs, lower, upper, rng = inputs
+    rv_inputs = [rng, *rv_inputs]
+
+    base_rv_op = op.base_rv_op
+    logcdf = _logcdf(base_rv_op, value, *rv_inputs, **kwargs)
+
+    # For left truncated discrete RVs, we don't want to include the lower bound in the
+    # normalization term
+    lower_value = lower - 1 if base_rv_op.dtype.startswith("int") else lower
+    lower_logcdf = _logcdf(base_rv_op, lower_value, *rv_inputs, **kwargs)
+    upper_logcdf = _logcdf(base_rv_op, upper, *rv_inputs, **kwargs)
+
+    is_lower_bounded = not (isinstance(lower, TensorConstant) and np.all(np.isneginf(lower.value)))
+    is_upper_bounded = not (isinstance(upper, TensorConstant) and np.all(np.isinf(upper.value)))
+
+    lognorm = 0
+    if is_lower_bounded and is_upper_bounded:
+        lognorm = logdiffexp(upper_logcdf, lower_logcdf)
+    elif is_lower_bounded:
+        lognorm = pt.log1mexp(lower_logcdf)
+    elif is_upper_bounded:
+        lognorm = upper_logcdf
+
+    logcdf_numerator = logdiffexp(logcdf, lower_logcdf) if is_lower_bounded else logcdf
+    logcdf_trunc = logcdf_numerator - lognorm
+
+    if is_lower_bounded:
+        logcdf_trunc = pt.switch(value < lower, -np.inf, logcdf_trunc)
+
+    if is_upper_bounded:
+        logcdf_trunc = pt.switch(value <= upper, logcdf_trunc, 0.0)
+
+    if is_lower_bounded and is_upper_bounded:
+        logcdf_trunc = check_parameters(
+            logcdf_trunc,
+            pt.le(lower, upper),
+            msg="lower_bound <= upper_bound",
+        )
+
+    return logcdf_trunc
+
+
 @_truncated.register(NormalRV)
 def _truncated_normal(op, lower, upper, size, rng, old_size, dtype, mu, sigma):
     return TruncatedNormal.dist(
diff --git a/tests/distributions/test_truncated.py b/tests/distributions/test_truncated.py
index 7502260dc8..53e933285b 100644
--- a/tests/distributions/test_truncated.py
+++ b/tests/distributions/test_truncated.py
@@ -26,7 +26,7 @@
 from pymc.distributions.truncated import Truncated, TruncatedRV, _truncated
 from pymc.exceptions import TruncationError
 from pymc.logprob.abstract import _icdf
-from pymc.logprob.basic import logp
+from pymc.logprob.basic import logcdf, logp
 from pymc.logprob.transforms import IntervalTransform
 from pymc.logprob.utils import ParameterValueError
 from pymc.testing import assert_moment_is_expected
@@ -165,6 +165,34 @@ def test_truncation_continuous_logp(op_type, lower, upper):
             assert np.isclose(xt_logp_fn(test_xt_v), ref_xt.logpdf(test_xt_v))
 
 
+@pytest.mark.parametrize("lower, upper", [(-1, np.inf), (-1, 1.5), (-np.inf, 1.5)])
+@pytest.mark.parametrize("op_type", ["icdf", "rejection"])
+def test_truncation_continuous_logcdf(op_type, lower, upper):
+    loc = 0.15
+    scale = 10
+    op = icdf_normal if op_type == "icdf" else rejection_normal
+
+    x = op(loc, scale, name="x")
+    xt = Truncated.dist(x, lower=lower, upper=upper)
+    assert isinstance(xt.owner.op, TruncatedRV)
+
+    xt_vv = xt.clone()
+    xt_logcdf_fn = pytensor.function([xt_vv], logcdf(xt, xt_vv))
+
+    ref_xt = scipy.stats.truncnorm(
+        (lower - loc) / scale,
+        (upper - loc) / scale,
+        loc,
+        scale,
+    )
+    for bound in (lower, upper):
+        if np.isinf(bound):
+            return
+        for offset in (-1, 0, 1):
+            test_xt_v = bound + offset
+            assert np.isclose(xt_logcdf_fn(test_xt_v), ref_xt.logcdf(test_xt_v))
+
+
 @pytest.mark.parametrize("lower, upper", [(2, np.inf), (2, 5), (-np.inf, 5)])
 @pytest.mark.parametrize("op_type", ["icdf", "rejection"])
 def test_truncation_discrete_random(op_type, lower, upper):
@@ -232,6 +260,38 @@ def ref_xt_logpmf(value):
     assert np.isclose(log_integral, 0.0, atol=1e-5)
 
 
+@pytest.mark.parametrize("lower, upper", [(2, np.inf), (2, 5), (-np.inf, 5)])
+@pytest.mark.parametrize("op_type", ["icdf", "rejection"])
+def test_truncation_discrete_logcdf(op_type, lower, upper):
+    p = 0.7
+    op = icdf_geometric if op_type == "icdf" else rejection_geometric
+
+    x = op(p, name="x")
+    xt = Truncated.dist(x, lower=lower, upper=upper)
+    assert isinstance(xt.owner.op, TruncatedRV)
+
+    xt_vv = xt.clone()
+    xt_logcdf_fn = pytensor.function([xt_vv], logcdf(xt, xt_vv))
+
+    ref_xt = scipy.stats.geom(p)
+    log_norm = np.log(ref_xt.cdf(upper) - ref_xt.cdf(lower - 1))
+
+    def ref_xt_logcdf(value):
+        if value < lower:
+            return -np.inf
+        elif value > upper:
+            return 0.0
+
+        return np.log(ref_xt.cdf(value) - ref_xt.cdf(lower - 1)) - log_norm
+
+    for bound in (lower, upper):
+        if np.isinf(bound):
+            continue
+        for offset in (-1, 0, 1):
+            test_xt_v = bound + offset
+            assert np.isclose(xt_logcdf_fn(test_xt_v), ref_xt_logcdf(test_xt_v))
+
+
 def test_truncation_exceptions():
     with pytest.raises(ValueError, match="lower and upper cannot both be None"):
         Truncated.dist(pt.random.normal())