A hydraulic screw tensioning device includes a cylinder supported on a machine part that is to be clamped by a threaded bolt and nut. A first annular piston is guided in a sealed manner in a cylinder element, is disposed on the change sleeve, and is supported against an inclined surface of a monolithic collar of the change sleeve. At least one second annular piston is guided in a sealed manner in a cylinder element, is disposed on the change sleeve, and is supported against the first annular piston. Respective, facing inclined axial annular surfaces on the annular pistons and on the cylinder elements or annular shoulders thereof are inclined in the same direction and are pressure-remote. Annular surfaces on the second annular piston or pistons and on the annular shoulders of the cylinder elements extend perpendicular to the cylinder axis and are pressurized.