Solid propellant is a high-energy composite material composed of solid particles, which can exhibit time dependent behaviors such as creep and stress relaxation during long-term storage. To model and analyze time dependent behavior of solid propellants, the modified soft-bond model (MSBM) based on the rate process theory (RPT) was implemented in Particle Flow Code (PFC). Numerical results show the predicted creep and stress relaxation behaviors by MSBM are in good agreement with experimental data, demonstrating that the MSBM can accurately capture time dependent behaviors in solid propellants. Furthermore, three categories of DEM samples were generated by varying formulations such as particle size, volume fraction and gradation, and a damage parameter was constructed to assess the characteristics of creep and stress relaxation. Among all formulations, the DEM simulation identified the graded formulation exhibiting the minimal damage parameter and optimal creep and stress relaxation resistance. These findings provide guidance for formula design of solid propellant.