A comprehensive numerical analysis of HMX/GAP pseudo-propellant combustion has been established to predict the propellant burning rate and detailed combustion wave structure over a broad range of ambient pressure, laser intensity, and propellant composition. The model takes into account various fundamental processes at scales sufficient to resolve the microscopic flame-zone physiochemistry. The thermochemical parameters of HMX and GAP are deduced from existing experimental data. Four global decomposition reactions of HMX and GAP in the condensed phase as well as subsequent reactions are included. In the gas phase, a detailed chemical kinetics scheme involving 74 species and 532 reactions is employed to describe the heat-release mechanism. The effect of the external CO2 laser on the propellant burning characteristics prevails at low pressures, but decreases at high pressures at which the conductive heat feedback from the gaseous flame to the condensed phase overrides surface absorption of radiation energy. The burning rate decreases with the addition of GAP at low pressures, even though GAP burns much faster than pure HMX. One factor contributing to this phenomenon is the rapid gasification of GAP displacing the primary flame away from the surface. Conversely, above a certain pressure level, the burning rate may be considerably enhanced by adding a small amount of GAP because of the higher surface temperature at which the exothermic decomposition of GAP plays a decisive role in providing energy to sustain propellant burning.