A method and apparatus for treating a fiber paper web in a press device wherein the web is guided through a press nip form between a press roll and a backing element in the form of a backing roll, and wherein the press roll includes a surrounding roll jacket comprised of plastic and a stationary cross head axially traversing the roll jacket. Preserving the roll jacket by cooling the roll jacket at least areawise in the axial direction of the roll jacket which increases the abrasion resistance of the roll jacket. Various devices for cooling the roll jacket include spraying coolant at the outer surface of the roll jacket, spraying coolant at the surface of a felt belt which then engages the roll jacket in a press nip, blowing air into the outlet end of the press nip between the roll jacket and the felt belt and/or blowing air into the space surrounding the outer surface of the roll jacket, e.g., the interior of the loop of the felt belt or the interior of a liquid collecting pan surrounding the roll jacket.