A self-consistent physical model has been developed to simulate the kinetics in a high-repetition frequency, discharge-excited Sr atom metastable-metastable transition laser. The main pumping mechanism for each upper laser level has bee n clarified: the upper level of 301μm is pumped mainly by the spontaneous and stimulated emissions from the higher levels in early discharge pulses, while th e upper levels of the other 3 laser lines are chiefly populated through the reco mbination between the univalent Sr ions and electrons in the afterglow, and the collision mixing between neutral He and Sr atoms in compound triplet. The quant itative results predicted by the model are found to be in good agreement with th e previous experimental results. Furthermore, the temporal behavior of each lase r pulse is explained successfully by the simulation results.