a radial press for workpieces with cylindrical outer surfaces has a plurality of pressing jaws arranged in a circle for radial movement towards the axis of the workpiece outer surface . a pressure ring acts on the pressing jaws so that when the pressure ring is axial displaced , the jaws will open and close . both the pressure ring and the pressing jaws each have two surface parts , having a wide setting angle and two surface parts having a narrow setting angle , wherein the surface parts having a wide setting angle are disposed firstly at the end faces and secondly between the surface parts having the narrow setting angle . in this way , when the pressing jaws are closed , the surface parts having the wide setting angle are deployed first , and then the surface parts having the narrow setting angle are deployed .