Comprehensive analysis of kinetic and fluid dynamic processes in flowing-gas diode pumped alkali lasers (DPALs) using two- and three-dimensional computational fluid dynamics (2D and 3D CFD) models is reported for Cs DPALs. The models take into account effects of temperature rise and losses of alkali atoms due to ionization. Various gas flow regimes and transverse and parallel flow-optics directions configurations are studied. Optimization of the Cs DPAL parameters, using 3D CFD modeling, shows that applying high flow velocity and narrowband pumping, maximum lasing power as high as 40 kW can be obtained at pump power of 80 kW for transverse flow configuration in a pumped volume of ∼ 0.7 cm3. At high pump power the calculated laser power is higher for the transverse scheme than for the parallel scheme because of a more efficient heat convection from the beam volume in the transverse configuration. The CFD models are applied to experimental devices and the calculated results are in good agreement with the measurements.