Abstract: A method and device for cutting out pieces of the desired shape having a cavity with a bottom wall at different levels from a block of plastic foam material. The block of foam material is compressed between a first plate having a relief form member corresponding in shape to the desired cavity and a die having an aperture of the desired contour. The part of the compressed block protruding through the aperture is compressed by the back form member corresponding to the different levels of the cavity and provided on a second plate on the other side of the die remote from the first plate. A straight edge cutting blade cuts the block flush with the die between the die and the second plate to obtain the piece of desired shape.