In order to verify the numerical model, which was developed to simulate the behavior of the two-phase fluid flow in a single fracture, the characteristic equation of relative permeability was incorporated into the developed numerical model, and the computed results were compared with the experimental results of the model test. As results of the sensitivity analysis on the roughness and the aperture size of fracture, the gas velocity was inversely proportional to the fracture roughness, and not proportional to the square of aperture size which is usually observed in single phase flow in a single fracture. The numerical model was applied to the underground LPG storage terminal in order to check the field applicability. The simultaneous flow of water and gas in accordance with the operation pressures in a single fracture near cavern was simulated by the model. It was shown that the leaked gas was able to be controlled in a single fracture neither by the pressure of operation nor by that of groundwater in case the fracture became smoother in roughness and smaller in aperture size.