Internal ballistic process of two-stage light-gas gun has been solved by many investigators using different approaches. This paper presents two different approaches to predict the interior ballistic parameters of such gun. The first approach is based on isentropic compression of the light gas in the gun pump, whereas the second approach depends on the theory for piston operated compressor in which shock wave was formed and heated the light gas. For each approach, the governing equations have been used to construct a computer program. Predicted time histories of gun parameters associated with gun firing are presented. The predicted results of each approach are compared with available experimental measurements of other investigators; good agreements are generally obtained. For both approaches, samples of the predicted time histories for powder chamber pressure, pump tube pressure, piston velocity and its travel along the gun tube, and projectile velocity and its travel along the barrel are presented for two calibers (12.7 and 28.6 mm), together with relevant analyses and discussions.