This work describes the development and application of a compressible multiphase flow model for the numerical simulation of multiphase explosions containing a dispersed particle phase. The model treats all phases as fully compressible, allows full non-equilibrium among phases, and properly models the mathematical characteristics of a dispersed particle phase in both the dense and dilute limits. Using the characteristic equations, a multiphase Riemann solver is developed as the basis for a Godunov-based numerical method. The Riemann solver is approximate, non-iterative, and applicable to all phases. A heuristic equation of state modeling the functional dependence of the dispersed phase pressure on volume fraction is proposed and applied. Using the techniques developed, two multiphase explosion simulations are performed and compared with experiment. Excellent agreement between the numerical and experimental results is found, providing confidence in the solution techniques developed. The sensitivity of the model to correlations for drag, heat transfer, and dispersed phase pressure are also investigated. Results from this analysis indicate that the functional dependence of dispersed phase pressure on volume fraction must be properly represented to obtain accurate simulation results in scenarios where particle-particle interactions are important. Further analyses investigate the effects of physical parameters including particle loading, size, and material on multiphase explosion dynamics. The results of this study indicate the significant effect these parameters have on the overall explosion dynamics, which is important to applications involving both inert and reactive particles.