- A general model that reproduces the output parameters of diode-pumped alkali lasers with different pump beam apertures and shapes is reported. Comprehensive experimental and theoretical parametric studies of static diode-pumped Cs lasers are presented, including the dependence of the output laser power and the beam quality factor M2 on the power of the pump beam for different shapes of the pump beam, pump-to-laser beam overlaps, and laser cell lengths. Two different pump lasers with circular and rectangular beam shapes and pump powers of 65 W and 7 W, respectively, were used in two sets of experiments. An optical model of multi-transverse mode operation of alkali vapor lasers [Opt. Express25, 19767 (2017)OPEXFF1094-408710.1364/OE.25.019767] was modified and applied to the experimental results. The values of the laser power and M2 predicted by the model are in good agreement with the measured values for a wide range of the laser parameters.