Abstract: Method of manufacturing a cylindrical sleeve provided with longitudinal internal grooves closed at at least one of their ends, these grooves being preformed by broaching in a section of reduced internal diameter of the sleeve blank delimited by two shoulders; To close the ends of the grooves at the level of at least one of the shoulders, the invention makes provision for the deformation of the latter by the pressing back of material in the direction of the axis of the sleeve so as to constitute a continuous annular bead of a depth at least equal to that of the grooves and for the subsequent boring of the sleeve to the required diameter so as to remove the excess part of this bead; Application in particular is to the machining of rotary valve sleeves for power-assisted steering gear.