- Three-dimensional computational fluid dynamics (3D CFD) modeling of subsonic (Mach number M ~ 0.2) and transonic ( M ~ 0.9) diode pumped alkali lasers (DPALs), taking into account fluid dynamics and kinetic processes in the lasing medium is reported. The performance of these lasers is compared with that of supersonic ( M ~ 2.7 for Cs and M ~ 2.4 for K) DPALs. The motivation for this study stems from the fact that subsonic and transonic DPALs require much simpler hardware than supersonic ones where supersonic nozzle, diffuser and high power mechanical pump (due to a drop in the gas total pressure in the nozzle) are required for continuous closed cycle operation. For Cs DPALs with 5 x 5 cm 2 flow cross section pumped by large cross section (5 x 2 cm 2 ) beam the maximum achievable power of supersonic devices is higher than that of the transonic and subsonic devices by only ~ 3% and ~ 10%, respectively. Thus in this case the supersonic operation mode has no substantial advantage over the transonic one. The main processes limiting the power of Cs supersonic DPALs are saturation of the D2 transition and large ~ 60% losses of alkali atoms due to ionization, whereas the influence of gas heating is negligible. For K transonic DPALs both the gas heating and ionization effects are shown to be unimportant. The maximum values of the power are higher than those in Cs transonic laser by ~ 11%. The power achieved in the supersonic and transonic K DPAL is higher than for the subsonic version, with the same resonator and K density at the inlet, by ~ 84% and ~ 27%, respectively, showing a considerable advantaged of the supersonic device over the transonic one. For pumping by rectangular beams of the same (5 x 2 cm 2 ) cross section, comparison between end-pumping - where the laser beam and pump beam both propagate at along the same axis, and transverse-pumping - where they propagate perpendicularly to each other, shows that the output power and optical-to-optical efficiency are not affected by the pump geometry. However, the output laser beam in the case of end-pumped DPALs has a homogeneous spatial intensity distribution in the beam cross section, whereas for transverse-pumped DPALs the intensity varies significantly along the pumping axis (perpendicular to the resonator optical axis) and hence is strongly inhomogeneous in the laser beam cross section. Thus, higher brightness and better beam quality in the far field is achieved for the end-pumping geometry. Optimization of the resonator geometry for minimal gas temperature rise and minimal intra-resonator intensity (corresponds to a low ionization rate) is also reported.