diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
index 8d561e377f2..38d3c6ec88c 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
@@ -438,6 +438,7 @@ struct Triangle_structure_sampler_for_triangle_mesh
   Vpm pmap;
   double min_sq_edge_length;
   const Mesh& tm;
+  CGAL::Random rnd;
 
   Triangle_structure_sampler_for_triangle_mesh(const Mesh& m,
                                                PointOutputIterator& out,
@@ -446,9 +447,12 @@ struct Triangle_structure_sampler_for_triangle_mesh
   {
     using parameters::choose_parameter;
     using parameters::get_parameter;
+    using parameters::is_default_parameter;
 
     pmap = choose_parameter(get_parameter(np, internal_np::vertex_point),
                             get_const_property_map(vertex_point, tm));
+    if (!(is_default_parameter(get_parameter(np, internal_np::random_seed))))
+      rnd = CGAL::Random(choose_parameter(get_parameter(np, internal_np::random_seed),0));
     min_sq_edge_length = (std::numeric_limits<double>::max)();
   }
 
@@ -549,7 +553,7 @@ struct Triangle_structure_sampler_for_triangle_mesh
 
   Randomizer get_randomizer()
   {
-    return Randomizer(tm, pmap);
+    return Randomizer(tm, pmap, rnd);
   }
 
   void internal_sample_triangles(double grid_spacing_, bool smpl_fcs, bool smpl_dgs)
@@ -609,6 +613,7 @@ struct Triangle_structure_sampler_for_triangle_soup
   double min_sq_edge_length;
   const PointRange& points;
   const TriangleRange& triangles;
+  Random rnd;
 
   Triangle_structure_sampler_for_triangle_soup(const PointRange& pts,
                                                const TriangleRange& trs,
@@ -616,7 +621,13 @@ struct Triangle_structure_sampler_for_triangle_soup
                                                const NamedParameters& np)
     : Base(out, np), points(pts), triangles(trs)
   {
+    using parameters::choose_parameter;
+    using parameters::get_parameter;
+    using parameters::is_default_parameter;
+
     min_sq_edge_length = (std::numeric_limits<double>::max)();
+    if (!(is_default_parameter(get_parameter(np, internal_np::random_seed))))
+      rnd = CGAL::Random(choose_parameter(get_parameter(np, internal_np::random_seed),0));
   }
 
   std::pair<TriangleIterator, TriangleIterator> get_range()
@@ -681,7 +692,7 @@ struct Triangle_structure_sampler_for_triangle_soup
 
   Randomizer get_randomizer()
   {
-    return Randomizer(triangles, points);
+    return Randomizer(triangles, points, rnd);
   }
 
   void internal_sample_triangles(double distance, bool, bool)
@@ -737,6 +748,12 @@ struct Triangle_structure_sampler_for_triangle_soup
  *     \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
  *   \cgalParamNEnd
  *
+ *   \cgalParamNBegin{random_seed}
+ *     \cgalParamDescription{a value to seed the random number generator}
+ *     \cgalParamType{unsigned int}
+ *     \cgalParamDefault{a value generated with `std::time()`}
+ *   \cgalParamNEnd
+ *
  *   \cgalParamNBegin{use_random_uniform_sampling}
  *     \cgalParamDescription{If `true` is passed, points are generated uniformly at random on faces and/or edges of `tm`.
                              If `do_sample_faces` is `true`, random points will be iteratively generated uniformly at random in the triangle of a face
@@ -898,6 +915,12 @@ sample_triangle_mesh(const TriangleMesh& tm,
  *     \cgalParamExtra{The geometric traits class must be compatible with the point range's point type.}
  *   \cgalParamNEnd
  *
+ *   \cgalParamNBegin{random_seed}
+ *     \cgalParamDescription{a value to seed the random number generator}
+ *     \cgalParamType{unsigned int}
+ *     \cgalParamDefault{a value generated with `std::time()`}
+ *   \cgalParamNEnd
+ *
  *   \cgalParamNBegin{use_random_uniform_sampling}
  *     \cgalParamDescription{If `true` is passed, points are generated in a random and uniform way
  *                           over the triangles of the soup.}
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_distance.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_distance.cpp
index c8d1040383d..d3d9fb023f4 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_distance.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_distance.cpp
@@ -269,7 +269,7 @@ void general_tests(const TriangleMesh& m1,
             << "\n";
 
   std::vector<typename GeomTraits::Point_3> samples;
-  PMP::sample_triangle_mesh(m1, std::back_inserter(samples));
+  PMP::sample_triangle_mesh(m1, std::back_inserter(samples), CGAL::parameters::random_seed(0));
   std::cout << samples.size()<<" points sampled on mesh."<<std::endl;
 
 }