This dissertation documents the building of computational propellant/ingredient models toward predicting AP/HTPB/Al cookoff events. Two computer codes were used to complete this work; a steady-state code and a transient ignition code Numerous levels of verification resulted in a robust set of codes to which several propellant/ingredient models were applied. To validate the final cookoff predictions, several levels of validation were completed, including the comparison of model predictions to experimental data for: AP steady-state combustion, fine-AP/HTPB steady-state combustion, AP laser ignition, fine-AP/HTPB laser ignition, AP/HTPB/Al ignition, and AP/HTPB/Al cookoff. A previous AP steady-state model was updated, and then a new AP steady-state model was developed, to predict steady-state combustion. Burning rate, temperature sensitivity, surface temperature, melt-layer thickness, surface species at low pressure and high initial temperature, final flame temperature, final species fractions, and laser-augmented burning rate were all predicted accurately by the new model. AP ignition predictions gave accurate times to ignition for the limited experimental data available. A previous fine-AP/HTPB steady-state model was improved to predict a melt layer consistent with observation and avoid numerical divergence in the ignition code. The current fine-AP/HTPB model predicts burning rate, surface temperature, final flame temperature, and final species fractions for several different propellant formulations with decent success. Results indicate that the modeled condensed-phase decomposition should be exothermic, instead of endothermic, as currently formulated. Changing the model in this way would allow for accurate predictions of temperature sensitivity, laser-augmented burning rate, and surface temperature trends. AP/HTPB ignition predictions bounded the data across a wide range of heat fluxes. The AP/HTPB/Al model was based upon the kinetics of the AP/HTPB model, with the inclusion of aluminum being inert in both the solid and gas phases. AP/HTPB/Al ignition predictions bound the data for all but one source. AP/HTPB/Al cookoff predictions were accurate when compared to the limited data, being slightly low (shorter time) in general. Comparisons of AP/HTPB/Al ignition and cookoff data showed that the experimental data might be igniting earlier than expected.