There are four regular star-polyhedra, known as the Kepler-Poinsot polyhedra, which are denoted by \(\{5/2, 5\}, \{5/2, 3\}, \{5, 5/2\}\) , and \(\{3, 5/2\}\) using the Schläfli symbol. Whether the surface of a polyhedron made of a flexible material such as paper can be flattened without cutting or stretching is a problem that has been investigated. This problem has been solved for all convex polyhedra by using moving creases to change the shapes of some faces, which follows from Cauchy’s rigidity theorem. For non-covex polyhedra, the problem has been solved only for special polyhedra, such as orthogonal polyhedra, in general condition, that is, under the condition of finite creases in each folded state. The surfaces of regular star-polyhedra are not convex and they have not been included by known results, to the best of our knowledge. Thus, we give continuous flattening motions of the surfaces for all four regular star-polyhedra.