Apparatus for processing a sheet of material such as cardboard intended for making a folding box or case, comprises a stamping plate for carrying the sheet and co-operable with a tool. The stamping plate lies on a table plate of a frame structure which has holders for releasably carrying a form which extends parallel to the table plate, and at least one bridge assembly which extends movably above the table plate. A carriage is carried on the bridge assembly and moves transversely with respect to the direction of travel thereof. The carriage carries at least one vertically movable pressure member directed towards the table plate.