Since all possible scenarios of shock initiation of explosives cannot be tested in experiments, a large number of shock initiation models, have been developed. In this study, some of the aspects of the mathematical and numerical modeling for single and double shock initiation modeling of heterogeneous explosives are considered.To study the grain size effect on the sensitivity, ignition and growth reactive flow modeling is performed for the shock to detonation transition（SDT） experiments on the three particle size formulations of pressed PBXC03 previously carried out to investigate the influence of the HMX particle size on the shock initiation and the subsequent detonation growth process for the explosive. All of the formulation studied had the same density but had different HMX grain sizes. A set of ignition and growth parameters is obtained for the three formulations. Only the coefficient G1 of the first growth term in the reaction rate equation is varied with the grain size while other parameters are kept the same for all formulations. It is found that the G1 decreases almost linearly with HMX particle size for PBXC03. Both experimental and numerical simulation results show that the shock sensitivity of PBXC03 decreases with increasing HMX particle sizes, for the sustained pressure pulses（around 4 GPa） as applied in the experiment.Later on the influence of a small change of porosity on shock initiation and the subsequent detonation growth process of the explosive PBXC03 were investigated. All solid explosives in practical use are more or less porous. Two explosive formulations of pressed PBXC03 having the same initial grain sizes but slightly different porosities（1% and 2%） were tested earlier by using the in-situ manganin piezoresistive pressure gauge technique. The numerical modeling of the experiments is performed using an ignition and growth reactive flow model. A reasonable agreement to the experimental results is obtained by increasing the growth parameter in LeeTarver ignition and growth reaction rate equation with porosity. Combining the experimental and the simulation results show that the shock sensitivity increases with porosity for PBXC03 having the same explosive grain sizes, for the pressures（about 3.1 GPa） as applied in experiments.Moreover, the reaction rate equation in Lee-Tarver ignition and growth model is studied. It has been noted that some of the parameters of reaction rate（RR） equation are correlated, making it difficult to parameterize and optimize. Therefore, a new RR equation for the ignition and growth model has been proposed which has fewer parameters, and provides the same functionality as the Lee-Tarver RR equation. The ignition term is retained as it is in the LeeTarver RR equation while the growth term has been modified. The growth term can be modeled with only two parameters when two-term RR equation is used. New parameter sets with less parameters have been determined for Composition B and PBXC03 explosives. The resulting pressure history plots are relatively smooth.During the multiple shocking of an explosive, the most prominent effect which is concerned with the performance of the explosive is the desensitization induced by the first shock. To find a simple numerical model that could reproduce all important features of previously reported shock desensitization experiments, an extension in Lee-Tarver reactive flow model is proposed. The additional parameters required for this extension can be calibrated for a typical explosive by experiments. The new model has been implemented in hydrodynamic code LS-DYNA as a user defined equation of state subroutine, and is available to simulate various kinds of situations involving explosives up to the limits and capabilities of LS-DYNA. Desensitization by preshocking in double shock experiments, reflected shock and detonation quenching experiments have been studied using the new model, and the calculation results qualitative agree with the reported experimental results.As an application of the desensitization model, the initiation of the heterogeneous explosives by shaped charge jets is studied. The previously reported shaped charge jet initiation experimental setups are simulated using LS-DYNA solver having the desensitization model been implemented as a user defined equation of state. The simulation results indicate that the desensitization effects caused by the shocks preceding the jet play a significant role in determination of the run to detonation distance for covered explosives initiated by jets. The failure in initiation in the first explosive sample that is in contact with the steel plate and initiation of second sample separated further by an air gap, during the penetration of jet, can be explained on the bases of the desensitization phenomena. The simulation qualitatively reproduces various shock interaction phenomenon occurring in explosives during penetration by shaped charge jet.Finally, a kind of mesoscopic model（DZK model） for shock ignition of solid heterogeneous explosives is examined in order to demonstrate its availability to account for the desensitization by preshocking in explosives. Since the mesoscopic model is based on the assumption of the elastic viscoplastic pore collapse mechanism, on the other hand, the desensitization mechanisms is also described usually in connection with the closure of pores, the ability of the mesoscopic model to predict the desensitization effects is therefore analyzed. For this purpose, the DZK model has been implemented in LS-DYNA as a user defined equation of state. For verification, the double shock, reflected shock and detonation quenching experiments have been modeled. The numerical results show that the model can qualitatively reproduce various features of the previously reported preshock desensitization experiments.