The study of deflagration to detonation transition (DDT) in explosives is of prime importance with regards to insensitive munitions (IM). Critical damage owing to thermal or shock stimuli could translate to significant loss of life and material. The present study models detonation and deflagration of a commonly used granular explosive: cyclotetramethylene-tetranitramine, HMX. A robust literature review is followed by computational modeling of gas gun and DDT tube test data using the Sandia National Lab three-dimensional multi-material Eulerian hydrocode CTH. This dissertation proposes new computational practices and models that aid in predicting shock stimulus IM response. CTH was first used to model experimental data sets of DDT tubes from both Naval Surface Weapons Center and Los Alamos National Laboratory which were initiated by pyrogenic material and a piston, respectively. Analytical verification was performed, where possible, for detonation via empirical based equations at the Chapman Jouguet state with errors below 2.1%, and deflagration via pressure dependent burn rate equations. CTH simulations include inert, history variable reactive burn and Arrhenius models. The results are in excellent agreement with published HMX detonation velocities. Novel additions include accurate simulation of the pyrogenic material BKNO3 and the inclusion of porosity in energetic materials. The treatment of compaction is especially important in modeling precursory hotspots, caused by hydrodynamic collapse of void regions or grain interactions, prior to DDT of granular explosives. The CTH compaction model of HMX was verified within 11% error via a five pronged validation approach using gas gun data and employed use of a newly generated set of P-α parameters for granular HMX in a Mie-Gruneisen Equation of State. Next, the additions of compaction were extended to a volumetric surface burning model of HMX and compare well to a set of empirical burn rates. Lastly, the compendium of detonation and deflagration models was applied to the aforementioned DDT tubes and demonstrate working functionalities of all models, albeit at the expense of significant computational resources. A robust hydrocode methodology is proposed to make use of the deflagration, compaction and detonation models as a means to predict IM response to shock stimulus of granular explosive materials.