diff --git a/numpyro/distributions/continuous.py b/numpyro/distributions/continuous.py
index 686c6ebde..d6565df68 100644
--- a/numpyro/distributions/continuous.py
+++ b/numpyro/distributions/continuous.py
@@ -2683,8 +2683,11 @@ def sample(
 
     @validate_sample
     def log_prob(self, value: ArrayLike) -> ArrayLike:
+        log_p = -jnp.log(self.high - self.low)
+        is_in_support = (value >= self.low) & (value < self.high)
         shape = lax.broadcast_shapes(jnp.shape(value), self.batch_shape)
-        return -jnp.broadcast_to(jnp.log(self.high - self.low), shape)
+        log_p = jnp.broadcast_to(log_p, shape)
+        return jnp.where(is_in_support, log_p, -jnp.inf)
 
     def cdf(self, value: ArrayLike) -> ArrayLike:
         cdf = (value - self.low) / (self.high - self.low)
diff --git a/test/test_distributions.py b/test/test_distributions.py
index 7edc19226..b98993425 100644
--- a/test/test_distributions.py
+++ b/test/test_distributions.py
@@ -4486,3 +4486,106 @@ def test_interval_censored_validate_sample(
             censored_dist.log_prob(value)
     else:
         censored_dist.log_prob(value)  # Should not raise
+
+
+def test_uniform_log_prob_outside_support():
+    d = dist.Uniform(0, 1)
+    assert_allclose(d.log_prob(-0.5), -jnp.inf)
+    assert_allclose(d.log_prob(1.5), -jnp.inf)
+
+
+@pytest.mark.parametrize(
+    "low, high", [(0.0, 1.0), (-2.0, 3.0), (1.0, 5.0), (-5.0, -1.0)]
+)
+def test_uniform_log_prob_boundaries(low, high):
+    """Test that boundary values are handled correctly."""
+    d = dist.Uniform(low, high)
+    expected_log_prob = -jnp.log(high - low)
+
+    # Value at lower bound (included): should have finite log prob
+    assert_allclose(d.log_prob(low), expected_log_prob)
+
+    # Value just above lower bound: should have finite log prob
+    assert_allclose(d.log_prob(low + 1e-10), expected_log_prob)
+
+    # Value at upper bound (excluded): should be -inf
+    assert_allclose(d.log_prob(high), -jnp.inf)
+
+    # Value just below upper bound: should have finite log prob
+    assert_allclose(d.log_prob(high - 1e-10), expected_log_prob)
+
+    # Value inside support: should have finite log prob
+    mid = (low + high) / 2.0
+    assert_allclose(d.log_prob(mid), expected_log_prob)
+
+    # Value below lower bound: should be -inf
+    assert_allclose(d.log_prob(low - 1.0), -jnp.inf)
+
+    # Value above upper bound: should be -inf
+    assert_allclose(d.log_prob(high + 1.0), -jnp.inf)
+
+
+@pytest.mark.parametrize("batch_shape", [(), (3,), (2, 3), (4, 2, 3)])
+def test_uniform_log_prob_broadcasting(batch_shape):
+    """Test broadcasting with different batch shapes."""
+    if batch_shape == ():
+        low = 0.0
+        high = 1.0
+    else:
+        low = jnp.linspace(0.0, 1.0, np.prod(batch_shape)).reshape(batch_shape)
+        high = jnp.linspace(1.0, 2.0, np.prod(batch_shape)).reshape(batch_shape)
+
+    d = dist.Uniform(low, high)
+
+    # Test with scalar value
+    value = 0.5
+    log_probs = d.log_prob(value)
+    assert log_probs.shape == batch_shape
+
+    # Test with batched value
+    if batch_shape:
+        value_batched = jnp.linspace(-0.5, 1.5, np.prod(batch_shape)).reshape(
+            batch_shape
+        )
+        log_probs_batched = d.log_prob(value_batched)
+        assert log_probs_batched.shape == batch_shape
+
+        # Check that values outside support return -inf
+        # Values < low should be -inf
+        below_low = low - 0.1
+        assert_allclose(d.log_prob(below_low), -jnp.inf)
+
+        # Values >= high should be -inf
+        at_high = high
+        assert_allclose(d.log_prob(at_high), -jnp.inf)
+
+
+@pytest.mark.parametrize("value_shape", [(), (5,), (3, 4), (2, 3, 4)])
+def test_uniform_log_prob_value_broadcasting(value_shape):
+    """Test broadcasting when value has different shapes."""
+    d = dist.Uniform(0.0, 1.0)
+
+    if value_shape == ():
+        values = 0.5
+    else:
+        values = jnp.linspace(-0.5, 1.5, np.prod(value_shape)).reshape(value_shape)
+
+    log_probs = d.log_prob(values)
+    assert log_probs.shape == value_shape
+
+    # Check that values inside support have finite log prob
+    inside_values = jnp.linspace(0.1, 0.9, np.prod(value_shape) if value_shape else 1)
+    if value_shape:
+        inside_values = inside_values.reshape(value_shape)
+    log_probs_inside = d.log_prob(inside_values)
+    assert jnp.all(jnp.isfinite(log_probs_inside))
+
+    # Check that values outside support have -inf
+    outside_values = jnp.linspace(-1.0, 2.0, np.prod(value_shape) if value_shape else 1)
+    if value_shape:
+        outside_values = outside_values.reshape(value_shape)
+    log_probs_outside = d.log_prob(outside_values)
+    # Values in [0, 1) should be finite, others should be -inf
+    mask_inside = (outside_values >= 0.0) & (outside_values < 1.0)
+    assert jnp.all(jnp.where(mask_inside, jnp.isfinite(log_probs_outside), True))
+    assert jnp.all(jnp.where(~mask_inside, log_probs_outside == -jnp.inf, True))