The roller screw mechanism is provided with a screw including an external thread, with a nut arranged about and coaxial with said screw, the nut including an internal thread, and with a plurality of rollers inserted between the screw and the nut and each including an external thread engaging the external and internal threads of said screw and of said nut. The screw is axially moveable in relation to the rollers. The flanks of the thread of the screw have a concave profile in cross section.