Abstract: The invention relates to apparatus for supporting or clamping bodies of irregular shape, (particularly large workpieces) comprising a clamping jaw, in the form of a box with axially moveable plungers extending from its work face, said plungers being supported in different axial positions, determined by contact with the surface of the workpiece, by a solid medium within the box. Known apparatus do not have positive means for locking the plungers in their positions. The invention provides a simple and effective locking arrangement in which the solid medium is a multiplicity of hard balls, each plunger is formed with ball-receiving cavities, and application of a pressure to the balls is transmitted via the ball-receiving cavities to lock said plungers.