This paper studied the two dimensional heat transfer characteristics of the melting process of a phase change medium(n-octadecane) , which is expected to be used in a solar energy storage system,by numerical simulation. The natural convection in the liquid and the transient heat conduction in the solid with the second and the third boundary conditions are both considered in the simulation. The influence of heat flux on the melting process, the temperature profiles in both phases and the melting front are predicted under the calculation conditions. The predictions are found to be reasonable compared with experiment. It is expected,this study will give some suggestion for the optimum design of the PCM (phase change material) container used in heat pipe type heat storage system.