Abstract. The elastic aftereffect and stress relaxation after testing in stable and metastable sheet steels of different structural classes subjected to monotonic and alternating loading under various conditions have been studied. Dependence of the material mechanical behavior and distribution of residual stresses on the strength, possibilities of phase transformations under load and sequence of alternating loading have been shown. A mathematical model for stamping test of sheet steels taking into account phase transformations and stress relaxation has been developed.