Abstract: A machine for the explosive forming of a workpiece of sheet material comprises a yoke-shaped frame with a base carrying a pressure cylinder whose piston is insertable from below into any of several cutouts in an overlying turntable in which dies with cavities spanned by respective workpieces are receivable. An overhanging arm of the frame supports a plate with a bottom recess confronting the cavity of an aligned die and has an upwardly extending supply channel closable by a sliding gate. In operation, with a workpiece clamped between the die and the plate, a force-transmitting medium is admitted into the recess and, with the sliding gate open, a charge provided with a detonation retarder is introduced through the channel with the aid of an igniter at the lower end of that piston which initiates its detonation, occurring after the piston has been withdrawn from the channel and the gate has been closed.