Abstract: A method of cutting stacked layers of compressible material utilizing a steel rule cutting die. An open cell foam member is placed in the area between spaced portions of the cutting die to define a flat upper surface substantially flush with the sharpened upper edge of the cutting die. The stacked layers of compressible material are placed on top of the foam member and on top of the sharpened upper edge of the die and the upper platen of the associated press is lowered to precompress the stacked compressible layers prior to the cutting operation by the die. The foam member is an open cell member and has a compressibility such that it maintains a flat upper face flush with the upper cutting edge of the die during the precompression of the layers and thereafter moves downwardly in a smooth translatory manner to allow the layer to be moved downwardly through the cutting die.