A band press for a fiber web contains a cylinder having a solid surface over which there is guided the fiber web, for instance a paper web, which experiences a pressing or squeezing action in conjunction with a felt or wire and a press band which is impervious for a pressurized fluid medium. To accomplish the pressing or contact action there is provided a press housing containing a plurality of pressure chambers or spaces for pressurized fluid medium and with such pressure chambers operating at different pressures. The paper web is guided in a manner such that it bears upon the surface of the cylinder. The press housing is provided at the location where there outbound or depart the bands with a sharp departure or runnoff edge by means of which the bands are separated from the paper web which continues to remain at the cylinder.