Considering the thermodynamical fluid mechanics in the gain medium and laser kinetic processes, a three-dimensional theoretical model of exciplex pumped Cs vapor laser with longitudinal and transverse gas flow is established. The slope efficiency of laser calculated by the model shows good agreement with the experimental data. The comprehensive three-dimensional distribution of temperature and particle density of Cs is depicted. The influence of pump intensity, wall temperature and fluid velocity on the laser output performance are also simulated and analyzed in detail, suggesting that a higher wall temperature can guarantee a higher output laser power while causing a more significant heat accumulation in the cell. Compared to longitudinal gas flow, the transverse flow can improve the output laser power by effectively removing the generated heat accumulation and alleviating the temperature gradient in the cell.