The invention relates to a roller screw mechanism comprising a screw (110) provided with an external thread; a nut (130) coaxially surrounding the screw (130) and provided with an internal thread; and rollers (120), each of which is provided with an external thread, each roller (120) being interposed between the screw (110) and the nut (130) so that the threads of the rollers mesh with the threads of the screw and of the nut; said roller screw mechanism being characterized in that the threads of the rollers are complementary to the threads of the screw and of the nut so that, at zero load, the threads of the rollers co-operate on both of their flanks with the threads of the screw and of the nut in a contact geometry having curvilinear segments.