A flexible press cover which has an additional strengthening element in at least one of its two end regions. As a result, in the end region, the tensile strength and the tensile rigidity in the circumferential direction are increased with respect to that hitherto known in such a way that it is no longer necessary to clamp the press cover end region in between two components. Instead, the press cover according to the present invention is suitable to be fixed to the outer circumferential surface of a rotatable supporting element belonging to the cover carrying disk without the aid of an outer ring, a clamping band, clamping filament or the like. In the most beneficial case, the arrangement for fixing the press cover to the aforementioned supporting element is completely free of any kind of fixing elements which would be associated with the cover outer surface.