A press cover or jacket includes at least one first polymer layer. The polymer layer contains or has been produced from a polyurethane, and the polyurethane has been formed from a prepolymer and a crosslinker. The prepolymer is a reaction product of naphthalene 1,5-diisocyanate or phenylene 1,4-diisocyanate and at least one polyol selected from a polycarbonate polyol, a polytetramethylene ether glycol, polyether polycarbonate polyol or mixtures thereof. A press using the press cover is also provided.