The press has a frame (1) in which parallel conical shafts are mounted for stamping heads (5) that are driven to and below axial press rollers (4). The heads carry a spherical extrusion die (7) interacting with press recesses (6) of the rollers. A detachable safety unit (12) is provided for the rollers and the heads deferred on the shafts. The safety unit includes a stop part (14) i.e. pressure-transmitting elastic body, rotatably and axially held in a common support (13) for the rollers and heads. The support is detachably connected with the frame in a direction of shafts.