A uniaxial nonlinear viscoelastic constitutive equation incorporating cumulative damage was developed and used to successfully model three highly filled composite solid propellants, two based on hydroxy terminated polybutadiene with an ammonium perchlorate oxidizer and the third on a glycidyl azide polymer with a phase stabilized ammonium nitrate oxidizer. The nonlinear component of the model consists of a strain rate term, a damage term and a nonlinear exponent. The cumulative damage function itself is calibrated using data from two constant strain rate tests at opposing extreme values of strain rate. Four parameters in the nonlinear viscoelastic model are calibrated at a reference strain rate (low rate of strain) for various conditions of cumulative damage and two parameters are calibrated at the opposing extreme rate of strain for the condition of total damage (i.e., when cumulative damage equals unity). The theoretical predictions at intermediate strain rates are very encouraging, providing a good correlation with the experimental stress-strain data measured under uniaxial constant strain rate loading conditions. The incorporation of cumulative damage theory into the nonlinear viscoelastic constitutive equation enables the strength and failure time to be quantitatively defined in terms of the damage history. Predicted values of strength versus failure time and strength versus constant strain rare at the condition when the cumulative damage equals unity, agree reasonably well with the observed experimental results.