Pressure wave supercharger (PWS) is widely used in different applications especially for charging the internal combustion engines. This device utilizes the pressure waves issued the exhaust manifold. These waves transmitted from the exhaust gas side to the air side causing compression effect required for charging process. The present work aims to build a mathematical model to address the behavior of PWS at a wide range of operating conditions. The proposed model employs the basic conservation equations of continuity, momentum and energy as well as the species transportation. The gas flow is treated as 1-D, time dependent, and non-reactive compressible fluid flow. These equations are solved together numerically by using two steps Lax-Wendroff scheme. This technique enables to simulate the pressure waves more accurately and precisely.  A computer code has been built to simulate the effect of many parameters on PWS performance. These parameters are dimensions and cells size, number of cells, rotational speed of PWS, engine speed and the exhaust gas pressure. Synchronization between the engine speed and PWS speed requires mathematical coupling between the engine cycle and PWS. Therefore, real cycle simulation is performed taking into consideration combustion processes, valve timing, and the amount of residual gases. The results of the present model are compared with another data to validate the model. The comparison shows fair agreement. Using PWS with internal combustion engines leads to enhancing the engine power, volumetric efficiency and reducing NOx emissions.