For precise design and optimization of the Q-switch solid-state laser system parameters, the computer dynamic model is useful. In the past, this problem was many times solved. Nevertheless, in most cases, as a time starting point of the rate equation, the moment of Q-switch opening was taken for the simulation. Therefore many initial parameters had to be estimated. To have a more complex view on the giant pulse generation, the initial point of a calculation must be derived in the moment of a flashlamp trigger. In our scheme, the designed system of four main differential rate equations describes the energy transfer from the pumping source - a capacitor to the output giant pulse. Designed model was used for the alexandrite active medium. The alexandrite laser system was Q-switched electro-optically and four differential equations gave the computer results. On the base of the computer and physical experiment, it can be summarized that the realistic model of the giant pulse solid-state laser was completed. This model could be simply implemented for other flashlamp solid-state laser systems.