The phenomenon of plastic deformation stabilization under cyclic loading, characterized by the attainment of a steady-state plastic strain amplitude, is considered. Cyclic tests are conducted on Grade 20 steel specimens under conditions of repeated loading, when the stress cyclically varied from zero to maximum tensile stress and cycle asymmetry coefficient is equal to zero, at various stress amplitudes (375, 400, 425, 440, 475, 485, and 490 MPa). A limiting case of stabilization is identified, where the material transitions to predominantly elastic behavior following accumulated plastic deformation. For the first time, a new constitutive model is proposed to predict this effect, which accounts for relaxation phenomena and is based on material-invariant parameters. The model demonstrates accurate predictive capability for the transition to a stabilized hysteresis response and the ultimate state of deformation, as confirmed by experimental validation.