Computer simulation is always an important means for studying laser, while laser theory is the basis of simulation. Although the semi-classical laser theory can accurately describe the generation process of laser, its complexity leads to a need of huge resources and time for computation. However, in particular cases, the influence of some factors on the laser system can be neglected. If a simpler model is employed to describe the laser system, the time of simulation can be shortened significantly. In order to simulate the laser system more efficiently, a simulation model of Q-switched solid-state laser is proposed in this paper. In this model, the time-domain function of Q switch is introduced, which represents the modulation of Q switch loss over time. Because the cross section of the Nd:YAG rod is circularly shaped, the resonator eigenmodes are assumed to be a Laguerre-Gaussian beam for simplicity. Then, any other laser beam can be formed by superposition of the eigenmodes of the resonator. These series of resonator eigenmodes are coupled with the rate equations of laser crystals. Finally, the distribution of pump light field inside the laser crystal is approximated as super Gaussian distribution. Based on this physical model, the influence of pump power and pump light field distribution on the output beam of multimode Q-switched solid-state laser is investigated. The simulation results are in good agreement with the experimental data, which explains the validity of the proposed model. For instance, with the increase of pump power, the output power of the laser increases, but the overall slope efficiency decreases. This is because the diffraction loss m,n of the lower order mode is less than the diffraction loss of higher order mode. When the pumping power increases, the higher order mode that starts to oscillate has lower utilization efficiency of pump energy. Therefore, the overall slope efficiency of the laser is reduced. In order to analyze the mode competition in the multimode Q-switched solid-state laser more comprehensively, the processes of laser pulse generation, relaxation oscillation and continuous oscillation are calculated as one full cycle. The laws of pulse power and beam quality factor versus time are obtained. For example, the maximum instantaneous output power of the relaxation oscillation is about 30 times the steady continuous output power. This law has a certain reference value when analyzing the damage threshold of laser optical element. In the pulse generation stage, the beam quality factor is close to 1, which explains the fact that the pulse field composition is nearly the fundamental mode of the laser. In the relaxation oscillation, the value of the beam quality factor changes irregularly with time, because mode competition is in a non-equilibrium state at this time. When stable continuous oscillation occurs, the mode competition achieves dynamic equilibrium, which means that the proportion of each mode is no longer changed in the output light field.