In an apparatus for pressing the grinding belt of a belt grinding machine to the upper surface of a workpiece, a pressing beam located above and extending transversely to the feed direction of the workpiece carries a row of positioning units having downwardly extending positioning rods for applying forces to an equalizing mat positioned between the lower ends of the rods and the inner side of the grinding belt to push the belt downwardly onto the top surface of the workpiece. The forces are transferred from the positioning rods to the equalizing mat by a row of pressure plates respectively associated with the positioning rods with the lower ends of the positioning rods lying loosely against the pressure plates. This achieves a simplified construction easing maintenance and repair and allows the equalizing pad to have the ability to uniformly distribute the forces onto the grinding belt and to have the flexibility needed to accommodate workpiece top surfaces of different shapes.