Abstract: A hydraulic press elastic stamping tool having a tool body with a recess wherein is situated a flat elastic diaphragm whose flange makes contact with the tool body, forming a closed chamber. That chamber communicates with a source of working fluid under pressure through ducts in the tool body. The end portions of the diaphragm flange form, in conjunction with the main body of the diaphragm, an aperture closed at one end and dimensioned several times smaller than the thickness of the diaphragm. The aperture, in cross section thereof, is smoothly curved with respect to the plane of the diaphragm toward the bottom of the recess and the closed end of the aperture is situated in the zone which is not subjected to tension strain when working fluid is delivered under pressure into the chamber.