A comprehensive computer model has been developed to simulate the plasma kinetics in a high-repetition frequency, discharge excited He-Sr recombination laser. A detailed rate equation analysis, incorporating about 80 collisional and radiative processes, is used to determine the temporal and spatial (radial) behavior of the discharge parameters and the intracavity laser field during the current pulse, recombination phase, and afterglow periods. The set of coupled first-order ordinary differential equations used to describe the plasma and external electrical circuit are integrated over multiple discharge cycles to yield fully self-consistent results. The computer model has been used to simulate the behavior of the laser for a set of standard conditions corresponding to typical operating conditions. The species population densities predicted by the model are compared with radial and time-dependent Hook measurements determined experimentally for the same set of standard conditions. The results predicted by the model are found to be in close agreement with previous theoretical analyses and experimental studies of the discharge kinetics and general operating characteristics of the He-Sr recombination laser. The initial or prepulse conditions in the discharge column are shown to be far from equilibrium with strong radial gradients of the buffer gas and strontium ground state densities and the heavy body and electron temperatures. During the current pulse, a large Sr + + population (>1021 m-3) is established across the central region of the discharge tube by stepwise electron impact collisions via the Sr*, Sr+, and Sr +* levels. Following the cessation of the current pulse and rapid cooling of the electron temperature, it is shown that a recombination nonequilibrium is established between the 62S1/2-52P1/2 states of Sr II during the Sr + + recombination period, resulting in a population inversion between these states and lasing action at 4305 Å. Although the optical gain on the lasing transition saturates soon after the onset of lasing, the general kinetics of the discharge column and the Sr+* population densities, including the laser levels, are largely determined by electronic collisions and radiative decay rather than by stimulated emission.