To produce a rolled steel product such as rolled steel bars for reinforcing concrete, steel containing carbon, manganese, silicon, aluminium and niobium is rolled in at least three passes. The total reduction during the three passes or the last three passes as the case may be is at least 20%. The temperature before, during and after rolling is regulated such that the elasticity limit and resilience at -120 DEG C of the rolled product (as calculated from the expressions: LE=1035+510C+192Mn+2270Nb-0.21T1-0.40T2-0.48T3-3.51D KCV=2202-2066C+23.20Mn-2064Nb-0.77T1-1.24T2-0.23T3-1.98D wherein C is the carbon content of the steel, Mn is the manganese content of the steel, Nb is the niobium content, if any, of the steel, T1 is the temperature of the steel before rolling, T2 is the temperature of the steel during rolling, T3 is the temperature of the steel after rolling, D is the diameter of the steel after rolling, LE is the elasticity limit, and KCV is the resilience at -120 DEG C) attain the desired high values.
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