diff --git a/RELEASE-NOTES.md b/RELEASE-NOTES.md
index f3dafb2bd0..9f4dbbe9e5 100644
--- a/RELEASE-NOTES.md
+++ b/RELEASE-NOTES.md
@@ -13,6 +13,7 @@
 - Add sampler stats `process_time_diff`, `perf_counter_diff` and `perf_counter_start`, that record wall and CPU times for each NUTS and HMC sample (see [ #3986](https://github.com/pymc-devs/pymc3/pull/3986)).
 - Extend `keep_size` argument handling for `sample_posterior_predictive` and `fast_sample_posterior_predictive`, to work on arviz InferenceData and xarray Dataset input values. (see [PR #4006](https://github.com/pymc-devs/pymc3/pull/4006) and [Issue #4004](https://github.com/pymc-devs/pymc3/issues/4004).
 - SMC-ABC: add the wasserstein and energy distance functions. Refactor API, the distance, sum_stats and epsilon arguments are now passed `pm.Simulator` instead of `pm.sample_smc`. Add random method to `pm.Simulator`. Add option to save the simulated data. Improves LaTeX representation [#3996](https://github.com/pymc-devs/pymc3/pull/3996)
+- SMC-ABC: Allow use of potentials by adding them to the prior term. [#4016](https://github.com/pymc-devs/pymc3/pull/4016)
 
 ## PyMC3 3.9.2 (24 June 2020)
 ### Maintenance
diff --git a/pymc3/smc/sample_smc.py b/pymc3/smc/sample_smc.py
index caa366346e..33b297c226 100644
--- a/pymc3/smc/sample_smc.py
+++ b/pymc3/smc/sample_smc.py
@@ -137,6 +137,7 @@ def sample_smc(
     _log = logging.getLogger("pymc3")
     _log.info("Initializing SMC sampler...")
 
+    model = modelcontext(model)
     if cores is None:
         cores = _cpu_count()
 
@@ -165,8 +166,10 @@ def sample_smc(
 
     if kernel.lower() == "abc":
         warnings.warn(EXPERIMENTAL_WARNING)
-        if len(modelcontext(model).observed_RVs) != 1:
+        if len(model.observed_RVs) != 1:
             warnings.warn("SMC-ABC only works properly with models with one observed variable")
+        if model.potentials:
+            _log.info("Potentials will be added to the prior term")
 
     params = (
         draws,
diff --git a/pymc3/smc/smc.py b/pymc3/smc/smc.py
index 264ffb2779..1e1e58c92d 100644
--- a/pymc3/smc/smc.py
+++ b/pymc3/smc/smc.py
@@ -17,6 +17,7 @@
 import numpy as np
 from scipy.special import logsumexp
 from theano import function as theano_function
+import theano.tensor as tt
 
 from ..model import modelcontext, Point
 from ..theanof import floatX, inputvars, make_shared_replacements, join_nonshared_inputs
@@ -100,9 +101,11 @@ def setup_kernel(self):
         Set up the likelihood logp function based on the chosen kernel
         """
         shared = make_shared_replacements(self.variables, self.model)
-        self.prior_logp_func = logp_forw([self.model.varlogpt], self.variables, shared)
 
         if self.kernel.lower() == "abc":
+            factors = [var.logpt for var in self.model.free_RVs]
+            factors += [tt.sum(factor) for factor in self.model.potentials]
+            self.prior_logp_func = logp_forw([tt.sum(factors)], self.variables, shared)
             simulator = self.model.observed_RVs[0]
             distance = simulator.distribution.distance
             sum_stat = simulator.distribution.sum_stat
@@ -120,6 +123,7 @@ def setup_kernel(self):
                 self.save_sim_data,
             )
         elif self.kernel.lower() == "metropolis":
+            self.prior_logp_func = logp_forw([self.model.varlogpt], self.variables, shared)
             self.likelihood_logp_func = logp_forw([self.model.datalogpt], self.variables, shared)
 
     def initialize_logp(self):
diff --git a/pymc3/tests/test_smc.py b/pymc3/tests/test_smc.py
index d88fcaf18d..f2b682e5ca 100644
--- a/pymc3/tests/test_smc.py
+++ b/pymc3/tests/test_smc.py
@@ -130,6 +130,14 @@ def abs_diff(eps, obs_data, sim_data):
                 observed=self.data,
             )
 
+        with pm.Model() as self.SMABC_potential:
+            a = pm.Normal("a", mu=0, sigma=1)
+            b = pm.HalfNormal("b", sigma=1)
+            c = pm.Potential("c", pm.math.switch(a > 0, 0, -np.inf))
+            s = pm.Simulator(
+                "s", normal_sim, params=(a, b), sum_stat="sort", epsilon=1, observed=self.data
+            )
+
     def test_one_gaussian(self):
         with self.SMABC_test:
             trace = pm.sample_smc(draws=1000, kernel="ABC")
@@ -157,6 +165,11 @@ def test_custom_dist_sum(self):
         with self.SMABC_test2:
             trace = pm.sample_smc(draws=1000, kernel="ABC")
 
+    def test_potential(self):
+        with self.SMABC_potential:
+            trace = pm.sample_smc(draws=1000, kernel="ABC")
+            assert np.all(trace["a"] >= 0)
+
     def test_automatic_use_of_sort(self):
         with pm.Model() as model:
             s_g = pm.Simulator(