A mathematical model for a three-tiered system consisting of solid, liquid and gas is derived for studying the combustion of RDX propellants. The resulting nonlinear two-point boundary value problem is solved by Newton's method with adaptive gridding techniques. In this study the burning rate is computed as an eigenvalue, which can remove the uncertainty associated with employing evaporation and condensation rate laws in its evaluation. Results are presented for laser-assisted and self-deflagration of RDX monopropellants and are compared with experimental results. The burning rates are computed over a wide range of ambient pressures and compare well with experimental results from one to ninety atmospheres. The burning rate is found to be proportional to the pressure raised to the 0.76 power. Sensitivity of the burning rate to initial propellant temperture is calculated and found to be extremely low, in agreement with past theoretical predictions and experimental data. Results for laser-assisted combustion show a distinct primary and secondary flame separated by a dark zone, the length of which is dependent upon the incident laser flux intensity.