A workpiece support has a simplified structure and can operate with improved dependability and reliability. The workpiece support has a rod, a sleeve body externally fitted on the rod and elastically deformable so as to shrink in diameter, a case member supporting the sleeve body, and an external peripheral hydraulic chamber formed on the external periphery of the sleeve body. A hydraulic cylinder is provided for moving the rod in the axial direction and oil passage are provided for connecting the hydraulic operating chamber of the hydraulic cylinder with the external peripheral hydraulic chamber when the piston member of the hydraulic cylinder has moved up to or to the vicinity of the stroke end thereof.