Abstract: A mechanical pipe expander having a pyramidal, polyhedronal cross-section, segments resting against the pyramidal surfaces which are displaceable in axial direction relative to the polyhedron, and grooves formed in the longitudinal centers of the edges of the polyhedron so that the side surfaces of the grooves represent guides for the correspondingly shaped segments. The segments are formed as dove tails on the leading end thereof over a length of about 5-30% of their total length and each of the side surfaces of the dove tail recesses slide on a side surface of two adjacent grooves formed in the polyhedron. The length of the grooves is limited to the path of displacement of the polyhedron with respect to the segments, and the ends of the segments facing away from the leading end are held by radially acting springs against the surfaces of the polyhedron.