Nonlinear stress relaxation is far more difficult to model than creep. The present work shows that in the case of a polymer, focusing on the material's nonaffine local strains and stresses provides a sound basis for modeling stress relaxation in a physically realistic way. This new, though still simplified, model (1) describes a clearly nonlinear (strain-dependent) behavior that only becomes linear at very low strains, (2) has the potential to predict faster stress relaxation than creep, (3) is the first to account for the effect of reduced differences between the initial and the final plateau modulus, as in the case of semicrystalline materials, which increase the longest relaxation times, (4) explicitly quantifies the effect of temperature, when one considers the whole distribution of relaxation times, (5) may be extended to also account for the effect of changes in free volume, and (6) ensure very fast computation of relevant physical parameters and extrapolated long time behavior at any temperature, from experiments near room temperature spanning only a few hours. All predicted features generally agree with known experimental behavior, and initial comparisons with experimental stress-relaxation modulus data for a poly(methylmethacrylate) validate the formulation to within relative errors of 1.34%. The model may nevertheless still be upgraded beyond the much simplified physical picture adopted here by relaxing most the present assumptions (e.g., by upgrading the two-level process description) and, eventually, by also taking into account the effect of the fast initial strain ramp up to its nominal value. The work also discusses in detail the values and physical meaning of the model parameters. POLYM. ENG. SCI., 54:404–416, 2014. © 2013 Society of Plastics Engineers