Considering the transformation from stored energy of electric capacitors to that of the laser medium, and introducing the temporal factor and three-dimensional spatial amplified spontaneous emission (ASE), numerical calculations have been performed to simulate the characteristics of the multi-segment amplifier (MSA), including temporal changes in the pumping balance between central and side flashlamp arrays, stored energy, gain coefficient and gain distribution of the MSA. The present numerical codes have been verified with the experimental data of LLNL, demonstrating the ability of the predicted performance for the MSA.