A stamping device (1), which in particular is arranged for stamping unfired ceramic substrates, has a die holder device (8) with a plurality of dies (4, 5, 6, 7), which for activation can be locked to the die holder device (8) and then jointly with it execute an axial stamping motion. A coupling device (18) which is remote-actuated is used for the locking. For the remote transmission of the actuation motion, a flexible mechanical connecting means is used, such as preferably a cable (16).