Considering the amplified spontaneous emission, the saturation effect and the energy distributions of the incident pump and seed lasers, a physical model is established to describe the kinetic process and the output performance of a four sided diode pumped alkali vapor laser amplifier. According to the experimental parameters of a single-side pumped configuration with a diffuse type hollow cylinder cavity, energy distributions in the cell and influences of several important factors are simulated and analyzed. The model is validated by comparing the simulation result with the experimental data, which shows the model can provide an effective way for designing an efficient diode four-side symmetrically pumped alkali vapor laser amplifier.