A code is developed to analyze a spherically symmetric underwater explosion. The arbitrary Lagrangian-Eulerian(ALE) Godunov scheme for two-phase flow is used to calculate numerical fluxes through moving control surfaces. For detonation gas of TNT and liquid water, the Jones-Wilkins-Lee(JWL) equation of states and the isentropic Tait relation are used respectively. It is suggested to use the Godunov variable to estimate the velocity of a material interface. The code is validated through comparisons with other results on the gas-water shock tube problem. It is shown that the code can handle generation of discontinuity and recovering of continuity in the normal velocity near the material interface during shock waves interact with the material interface. The developed code is applied to analyze a spherically symmetric underwater explosion. Repeated transmissions of shock waves are clearly captured. The calculated period and maximum radius of detonation gas bubble show good agreements with experimental and other numerical results.