A diode pumped alkali laser (DPAL) provides a significant potential for construction of high-powered lasers. Until now, a series of models have been established to analyze the kinetic process and most of them are based on the end-pumped alkali laser system in which the vapor cell are usually cylindrical and cuboid. In this paper, a mathematic model is constructed to investigate the kinetic processes of a diode pumped thin-disk cesium vapor laser, in which the cesium vapor and the buffer gases are beforehand filled in a sealed glass cell with a thin-disk structure. We systemically study the influences of the cell temperature and cell thickness on the output features of a thin-disk DPAL. Further, we study the thin-disk DPAL with the W-shaped resonator and multiple-disk configuration. To the best of our knowledge, there have not been any similar reports so far.