Abstract: This invention relates to a machining device incorporating a blank-press connected to the tool and to a blank-press for such a device, wherein said blank-press is provided with an annular chamber surrounding said tool and obturated opposite the workpiece by a flat face traversed by a plurality of orifices; said annular chamber comprises means for connection to a source of fluid under pressure; and said fluid emerging from the annular chamber through said orifices between the flat face of the workpiece and the flat face of the annular chamber creates a fluid film for lift. The invention is more particularly applicable to the trimming of stacks of sheet metal plates.