To understand and predict the response of explosive materials, numerical models are utilized to simulate various scenarios. Various hazard and vulnerability scenarios for explosives involve multiple shock compression. In the present study, a kind of mesoscopic model for shock ignition of solid heterogeneous explosives is examined in order to demonstrate its availability to account for the desensitization caused by multiple shocks in explosives. Since the mesoscopic model is based on the assumption of the elastic viscoplastic pore collapse mechanism, and on the other hand the desensitization mechanism is also usually described in connection with the closure of pores, the ability of the mesoscopic model to predict the desensitization effects must be analyzed. For this purpose, the mesoscopic model has been implemented in a hydrodynamic code (LS-DYNA) as a user-defined equation of state. For verification, the double shock, reflected shock and detonation-quenching experiments have been modeled and simulated. The data show that the model can reproduce various features of some of the previously reported experiments involving the preshock desensitization of solid explosives.