A method of producing an axially extending rolled steel member for use as prestressing steel member and having a generally circular transverse section with an axially extending core zone (K) enclosed by an axially extending annular rim zone (R) and comprising the steps of forming the steel member with a C content in the range of 0.50 to 0.80%, a Si content in the range of 0.20 to 0.50%, a Mn content in the range of 0.30 to 0.80%, hot rolling the steel member in a rolling mill with a finishing stand having an outlet, removing the rolled member from the outlet of the finishing stand at the final rolling temperature and selecting the final rolling temperature in the range of 860.degree. to 1060.degree. C., surface quenching in a single operation the rolled member at the rolling temperature from the finishing stand using a cooling medium so that the rim zone (R) is transformed immediately into martensite while maintaining the heat content in the core zone (K) so that the heat content does not temper the martensite rim zone during subsequent cooling beyond the range of the intermediate stage, and surface quenching and tempering the steel member so that the surface temperature of the rim zone, depending on the diameter of the steel product, is in the range of 400.degree. and 500.degree. C. in the time interval between the second and sixth second following the commencement of surface quenching.