Abstract: A new reaction rate function model was developed to represent explosive initiation process based on Kim elastic-plastic pore collapse hot spot reaction model by analyzing explosive reaction rate function models. Parameters of the developed reaction rate function model were determined by using genetic algorithms as well as one dimensional Lagrangian shock to detonation pressure curv. The new model was validitied by comparision of simulation results between the new model and the Forest-Fire reaction rate function model. PBX-9404 shock initiation and detonation process was numerically simulated by embedding the new reaction rate function model into finite element analysis program. Influences of porosity and grain size change on initiation and detonation behaviours of explosive were analyzed by the numerical simulation results in the event that explosive was loaded by applied shock.