Abstract: A surface sleeve for a rotogravure cylinder or an offset cylinder is produced by mounting a basic sleeve (20) on a supporting mandrel (10). Both the outer peripheral surface of the mandrel and the inner and outer surfaces of the basic sleeve are circularly cylindrical. On the nickel cylinder (20), a thin layer (21) of copper or nickel is deposited electrolytically, and on top of this layer an outer copper layer (22), preferably high-gloss copper, is deposited. In the case of rotogravure, this outer copper layer has a thickness which equals or slightly exceeds the desired maximum well depth of the printing pattern later to be made in the outer surface of the surface sleeve. In the case of offset printing, the outer copper layer is coated with a chrome layer in which the printing pattern is etched.