A device for punching work pieces in an internal high-pressure forming tool includes a punching die guided displaceably in a bore of the forming tool. The device also contains a drive with which the punching die is moved back and forth between the in-use position and the non-use position. In order to facilitate, in a simple and space-saving manner, the punching of work pieces in the internal high-pressure forming tool, the drive contains a pressure fluid and a pressure transfer device that can be elastically expanded via the pressure fluid between a base firmly attached to the tool and a punch head of the punching die. The pressure transfer device abuts a partition at least indirectly at the punch head.