New phenomenological model of accumulation of plastic deformation under repeated cyclic loading for metals based on a notion of the characteristic time as a material property is proposed. Incorporation of the temporal parameter into deformation law allows one to predict the adaptability effect of material at a low-cycle loading, which is defined by the stabilization process of accumulated plastic deformation after multiple loading cycles. Some of the known experimental data for the quenched steel-50 with the observed adaptability effect on the basis of the proposed model are analyzed. Obtained values of the characteristic time for each of the steel grades differ essentially depending on the way of treatment. It is shown that the parameter of temporal sensitiveness of material, presented in the relaxation model of plasticity, can serve as an effective tool for description the stabilization phenomenon and reflection the technological actions towards material.