This paper develops a three level model for a continuous wave diode pumped alkali laser by creating rate equations based on a three level system. Differential equations for intra-gain pump attenuation and intra-gain laser growth are developed in the fashion done by Rigrod. Using Mathematica 7.0, these differential equations are solved numerically and a diode pumped alkali laser system is simulated. The results of the simulation are compared to previous experimental results and to previous computational results for similar systems. The absorption profile for the three level numerical model is shown to have excellent agreement with previous absorption models. The lineshapes of the three level numerical model are found to be nearly identical to previous developments excepting those models assumptions. The three level numerical model provides results closer to experimental results than previous systems and provides results which observe effects not previously modeled, such as the effects of lasing on pump attenuation.