A gripping device for a handling device of a processing machine for handling plate-form workpieces, including a carrying structure at least one gripper bar, and gripping elements. The at least one gripper bar is arranged on the carrying structure and is oriented for displacement along an axis of the carrying structure and extends along a further axis of the carrying structure which differs from the displaceable axis. The gripping elements are arranged on an underside of the at least one gripper bar for handling the at least one workpiece. In an end region the at least one gripper bar has at least one gripper finger which, as viewed in a longitudinal axis of the at least one gripper bar, is designed tapered in relation to a main portion of the at least one gripper bar.