Proper mechanical model selection is critical in tunnel support design and stability analysis, especially to reflect the creep and strain-softening behavior of soft rock. We present a coupled nonlinear Burgers strain-softening (NBSS) model and numerical calculation method to investigate the coupled effects of creep and strain-softening of soft rock tunnels. The nonlinear elastic-viscous model is used to simulate the steady creep behavior of mudstone, and the nonlinear viscoplastic strain-softening model is used to simulate the accelerated creep behavior and post-peak strength attenuation behavior. The experimental results show that the viscoplastic parameters and post-peak softening parameters of mudstone are highly sensitive to confining pressure and exhibit nonlinear characteristics. The accelerated creep curve obtained by the numerical calculation is consistent with the experiments, which verifies the model reliability. We use the NBSS and nonlinear Burgers Mohr-Coulomb (NBMC) models to calculate the plastic zone distribution characteristics and deformation law. The distribution of the plastic zone calculated by the NBSS model is larger with more localized fractures. The NBSS model is useful for studying the evolution of stress and displacement fields of complex surrounding rock mass, which provides important theoretical guidelines for the support design and stability analysis of soft rock tunnel engineering.