A one-dimensional, steady-state numerical model of the combustion of homogeneous solid propellant has been developed. The combustion processes is modeled in three regions: solid, two-phase (liquid and gas) and gas. Conservation of energy and mass equations are solved in the two-phase and gas regions and the eigenvalue of the system (the mass burning rate) is converged by matching the heat flux at the interface of these two regions. The chemical reactions of the system are modeled using a global kinetic mechanism in the two-phase region and an elementary kinetic mechanism in the gas region. The model has been applied to RDX, HMX and GAP. There is very reasonable agreement between experimental data and model predictions for burning rate, temperature sensitivity, surface temperature, adiabatic flame temperature, species concentration profiles and melt-layer thickness. Many of the similarities and differences in the combustion of RDX and HMX are explained from sensitivity analysis results. The combustion characteristics of RDX and HMX are similar because of their similar chemistry. Differences in combustion characteristics arise due to differences in melting temperature, vapor pressure and initial decomposition steps. A reduced mechanism consisting of 18 species and 39 reactions was developed from the Melius-Yetter RDX mechanism (45 species, 232 reactions). This reduced mechanism reproduces most of the predictions of the full mechanism but is 7.5 times faster. Because of lack of concrete thermophysical property data for GAP, the modeling results are preliminary but indicate what type of experimental data is necessary before GAP can be modeled with more certainty.