Based on the Monte Carlo rays tracing method, the three dimensional numerical model of pump distribution in Nd:glass disc amplifier is developed. In addition, combined with the other numerical models of Xe flashlamp charge/discharge circuit, amplified spontaneous emission, and laser pulse amplification, the whole work process of Nd:glass disc-amplifier is numerical simulated in detail to realize the whole process of the energy storage to the amplifying of Nd:glass disc amplifier. Based on the results of numerical simulation, the designed Nd:glass disc amplifier is used in the experiments of 5 PW Ti:sapphire chirped pulse amplifier, and the experimental results are in good accordance with the calculated consequence.