A roller screw mechanism has a screw provided with an outer thread, a nut surrounding and coaxial with the screw, the nut being provided with an inner thread, a plurality of rollers radially disposed between the screw and the nut and each provided with an outer thread engaging the outer and inner threads and with two outer gear teeth, and two synchronization gear teeth meshing with the gear teeth of the rollers. The mechanism further includes one retaining cage for the rollers including a plurality of pockets spaced apart one with another in the circumferential direction. At least the outer thread of each roller is located inside the associated pocket of the cage.