Abstract: In the ZWT nonlinear viscoelastic constitutive model, additional Maxwell elements were incorporated to establish a nonlinear generalized Maxwell model (NLGMM), and the NLGMM was numerically discretized. Based on the Nelder-Mead simplex algorithm, the constitutive parameters were optimized and validated with tensile test data of hydroxyl terminated polyethe (HTPE) solid propellant at different constant displacement rates. The differences in true stress calculation with engineering strain rates and true strain rates were analyzed. The results show that after numerical discretization and parameter optimization, the established NLGMM could effectively describe mechanical behavior of HTPE solid propellant. The maximum relative error between the calculated true stress and the test results was not higher than 6%. When the deformation of HTPE solid propellant was small (the true strain was not greater than 0.1), the relative error between the true stress calculation with engineering strain rates and that with true strain rates did not exceed 5%, indicating that the nonlinear effects caused by material deformation could be neglected and the material parameters of NLGMM could be calculated with engineering stress-engineering strains and engineering strain rates. When HTPE solid propellant underwent large deformation (the true strain was not less than 0.4), the true stress calculation with engineering strain rates was not less than 1.33 times that with true strain rates, and the nonlinear effects caused by material deformation could not be ignored. The material parameters of NLGMM should be calculated with true stress-true strains and true strain rates.