A truing operation for straightening out of true work pieces such as crankshafts, must not again reduce the fatigue strength of the work piece achieved in a previous strengthening operation. This is achieved by a truing operation, wherein locally bounded compressive residual stresses are induced in a surface layer zone of the work piece by a hardening operation, whereby the respective out of true deformation of the work piece is at least reduced. The truing operation is repeated until the out of true deformation is eliminated. The compressive residual stresses are induced in a surface layer zone of the work piece by a locally limited hardening operation, e.g. a surface strengthening rolling operation. By appropriately varying the extent of hardening or the rolling force respectively, any out of true deformation may be even completely eliminated. A machine for performing the method is also disclosed.