A model which can simulate the pump dynamics process of the main amplifiers in million joules laser facility is built based on Monte Carlo algorithm and a ASAP software. The model contains 3D airspace and 1D time domain, and the evolution of the distribution of the energy in light pass surface in different pumping time with complete absorption on cladding is calculated, which is the same with the results mentioned in previous articles proving the accuracy of the model. The comparisons of average small signal gain coefficient are made between the cases when the residual reflection in cladding is taken into consideration or not. The results show that there is no significant difference when residual reflectivity is below 0.05%. The value of calculated average small signal gain coefficient with residual reflection is 6 percentage smaller than the measured value(4.42/m), which results from the use of part approximation during the simulation, the unconsidered spectrum of spontaneous radiation,the subsurface damage in the actual Nd:phosphate glass and so on.