A physical model that describes the gain performance of high power solid state laser amplifier has been presented. The model is time-and spectrum-related and consists in four key factors that describes the energy conversion of amplifier, i.e., (1) pump source, (2) cavity transfer, (3) gain medium, and (4) gain performance and energy storage efficiency. With this model, the parameters of pumping sources and gain medium for 4×2×3 amplifier have investigated in detail. The calculation results indicate that the small signal gain coefficient and energy storage efficiency are about 5.0% cm-1 and 3.0%, respectively, which meet design performance requirement.