- Experimental and theoretical study of the influence of the pump-to-laser beam overlap, a crucial parameter for optimization of optically pumped alkali atom lasers, is reported for Ti:Sapphire pumped Cs laser. Maximum laser power > 370 mW with an optical-to-optical efficiency of 43% and slope efficiency ~55% was obtained. The dependence of the lasing power on the pump power was found for different pump beam radii at constant laser beam radius. Non monotonic dependence of the laser power (optimized over the temperature of the Cs cell) on the pump beam radius was observed with a maximum achieved at the ratio ~0.7 between the pump and laser beam radii. The optimal temperature decreased with increasing pump beam radius. A simple optical model of the laser, where Gaussian spatial shapes of the pump and laser intensities in any cross section of the beams were assumed, was compared to the experiments. Good agreement was obtained between the measured and calculated dependence of the laser power on the pump power at different pump beam radii and also of the laser power, threshold pump power and optimal temperature on the pump beam radius. The model does not use empirical parameters such as mode overlap efficiency and can be applied to different Ti:Sapphire and diode pumped alkali lasers with arbitrary spatial distributions of the pump and laser beam widths.