Abstract: In this paper, we first built a 3D model for diode pumped alkali vapor laser (DPAL) based on the three-level rate equations and split-step beam propagation method, which can be used to simulate the kinetic process of end-pumped single-pass Rb vapor laser. This model considered beam propagation and light interaction with matter respectively. This model was solved by the iteration method. As an example, the distribution for population inversion which is under the optimal mode-matching and gain through different axis was investigated. Then we calculated the influence of mode-matching on the threshold and explained this influence by the distribution of particles and light field distribution. Finally we analyzed the influence of the length of gain cell on threshold characteristics. It turned out that the parameter of the cavity is related to the mode of pumped laser. The threshold will be the minimum value when the cavity parameters and the pumped laser mode are properly selected.