Abstract: A vacuum gripper is provided for picking up and setting down unit loads by layer, comprising a surface having suction openings, connected to a vacuum supply, and device for temporarily connecting the suction openings. The vacuum gripper comprises at least two air channels, connecting suction openings. Each air channel is connected by a valve to a central, linear vacuum supply channel connected to the vacuum supply. The valve comprises at least one tappet, whose movement makes possible controlling opening and closing the valve. The tappets are arranged in a straight row, and are automatically moved in a position where the valve is closed. The tappets are functionally connected to a mechanical actuating device, extending along the row, comprising mechanically movable control elements for sequential actuation. The control elements automatically restore the tappets to a position where the valve is closed, making possible closing the related valves sequentially.