A grinding or sanding machine for grinding or sanding a surface of a workpiece includes a transportation device for transporting a work piece, a revolving grinding or sanding belt, and at least one pressure beam for exerting a pressure toward the transportation device. A plate is provided that is movable in a plane perpendicular to the direction in which pressure is exerted. The plate is disposed between the belt and the pressure beam. A drive device randomly moves the plate in plate movement directions in terms of either or both direction and speed.