The present invention is directed to a roll cover for a calender or press roll for treating a material web. The roll cover includes a layer of elastomeric material having filaments running approximately longitudinally with respect to a web run direction and transversely to the web run direction embedded for reinforcement, and at least one layer of additional reinforcing filaments embedded in at least some sections of the elastomeric layer. The additional reinforcing filaments run at an angle between 20° and 70° with respect to the web run direction. The layer is arranged to form roll ends connectable to a roll axle. The instant abstract is neither intended to define the invention disclosed in this specification nor intended to limit the scope of the invention in any way.