A rubber cylinder sleeve has a rubber covering with a layer construction which includes, at a distance from the outer surface, compressible layer elements and layer elements which influence the stiffness (S), such as filaments/yarns or fabric structures. The layer elements which influence the stiffness (S), are incorporated uniformly in the circumferential direction but are prestrained to various degrees in a defined manner in the direction of the sleeve axis, so that a stiffness profile is produced across the sleeve width, which profile is symmetrical with respect to the center of the sleeve width.