Numerical simulation of high-power gas lasers requires the integration of a variety of numerical techniques; simultaneous solutions must be obtained to a large set of ordinary differential equations, and several nonlinear partial differential equations. A family of codes employing similar methods has been devised and has demonstrated remarkable success in predicting laser performance over a broad range of parameters. We describe here the appropriate techniques for dealing with gas kinetic equations, the steady-state Boltzmann equation, and physical optics. Modeling of both

-beam pumped and

-beam sustained discharge-pumped lasers is described; complex electron kinetic processes are included. Results are shown for both krypton-fluoride and xenon-fluoride lasers.