A belt grinding machine is described for the grinding of chipboard, fibreboard, faced board for similar boards in which the upper part of the housing can be raised and lowered relative to the lower part of the housing by a lifting device for adaptation to different board thicknesses. Spaced apart distance pieces or spacers are provided between the two parts of the housing to enable the basic board thickness to be selected. In order to ensure that boards of widely varying thicknesses can be machined with a grinding accuracy which meets the highest requirements, even when the boards that are supplied have relatively large thickness variations, a vertically steplessly adjustable clamping element, which is acted on by a pressure fluid, is associated with each spacer. In the lowered state of the upper part of the housing the clamping device clamps the upper part to the lower part with the spacers being trapped therebetween. The pressure of the pressure fluid supplied to the clamping devices is adjustable.