A two-dimensional melting process of a solid phase change material is investigated theoretically. The material contained in a rectangular enclosure heated from one side, while all the other sides are assumed to be adiabatic ones. In this study convection mode was considered to be the dominant mode of heat transfer within the melted region, except within the region very close to the solid surface at the bottom where conduction mode was only taken into considerations. It was found that the obtained results are in good agreement with previous ones. Finally the present analysis was used to predict the melted fraction of the phase change material and hence the amount of stored energy.