The hole punching machine has a multiple tool group (2). It includes a stamping device (6) between the striker and the multiple tool group. The stamping unit is carried by a fixed structure (7). It transmits the pressure from the striker to a punching tool. There are turning devices (8) to turn the device and the tool group round an axis (A) to select the striking point and the tool of which the strike is made. There are also devices (11) to select the specific item to be turned. The multiple die group is turned round the same axis (A) by other devices (61).