Based on the energy-level structure of quasi-three-level Yb ion，an amplified spontaneous emission model in pumping process is set up. The stored energy density distribution and the energy that can be extracted in Yb：YAG crystal are calculated. Our calculation，which is based on the laser rate equations and the theory of anglular spectrum propagation，can simulate time-resolved evolution of the spatial intensity distribution and M2 factor of the laser pulses. At the same time，an experiment in laser diode-pumped Q-switched rep-rated Yb：YAG disk laser was performed. This model was proved to be correct by comparing the results of the experiment and calculation，which will be helpful in designing active Q-switched solid laser.