A printing sleeve (30) for a rotogravure or flexo printing roll (31) is provided that has a slightly conical or tapered geometry wherein the inner diameter at one end is slightly smaller than the inner diameter at a second end. Similarly, the printing roll is provided with a slightly conical geometry or tapered diameter as well wherein the outside diameter at one end is slightly smaller than the outside diameter at the other end. The larger end of the printing sleeve is mounted over the smaller end of the printing roll and the sleeve is pushed forward either manually or mechanically until the larger end of the printing sleeve is disposed over the larger end of the printing roll. A key/slot (6) combination may be provided on the inside surface of the printing sleeve and outside surface of the printing roll to ensure proper alignment. An apparatus also is provided for mounting a printing sleeve over a printing roll which includes two support bearings (7;8) for mounting the opposing ends of the printing roll or printing axle. A clamp (9) is provided to positively clamp the larger end of the printing roll against its respective support bearing. A support arm (10) is further provided to balance the printing roll thereby enabling the lowering or release of the support bearing supporting the opposing end of the printing roll. After the sleeve has been partially inserted over the printing roll, the support bearing is then raised and the support arm is released. Then, a push adaptor (11) is provided for forcing the printing sleeve in place over the printing roll with a predetermined amount of force.