Abstract: Some embodiments are directed to a machine tool holding device for clamping a piece to be clamped that includes a contact surface. The holding device includes at least one claw intended to come into contact with the contact surface of the piece to be clamped. The claw includes a plurality of clamping plates stacked on each other, and each including on their edge a clamping surface arranged to be in contact with a portion of the contact surface of the piece to be clamped.