A turret punch press (1) includes an upper and lower turret (15, 17) for respectively supporting a plurality of punches (11) and dies (13); the punches (11) are arranged two-dimensionally in a punch mounting region on the upper turret (15) and the dies (13) are arranged two-dimensionally in a die mounting region on the lower turret (17). The turret punch press further includes a ram (21) and a striker (19) for striking the punches. The striker (19) is provide on a bottom of the ram (21) so as to be movable in two horizontal directions (X, Y) above the punches indexed in a processing region. In the turret punch press, when the turret is indexed in the processing region, many punches and dies are sinultaneously indexed in the processing region. Thus, by moving the striker in two horizontal directions above the punches indexed in the processingregion, many successive punch operations can be quickly performed without intermediate rotation of the turrets.