This study is focused on the modeling of two phase fluid flow system in the electrode of hydrogen gas generator. The characteristics of hydrogen gas generation was studied in view of efficiency of hydrogen gas generation rate and a tendency of gas flow through the riv of electrode. Since the flow rate of generated gas is the most crucial in determining the efficiency of hydrogen gas generator, we adopted the commercial analytical program of COMSOL $Multiphysics^{TM}$ to calculate the theoretical flow rate of hydrogen gas from the outlet of gas generator.