Two-dimensional melting of a solid phase change material in a rectangular enclosure heated from one side is simulated numerically. The simulations are carried out by dividing the process in a large number of quasi-static steps. In each quasi-static step, steady-state natural convection in the liquid phase is calculated by directly solving the governing equations of motion with a finite difference technique. This is used to predict the shape and motion of the solid-liquid boundary at the beginning of the next step. The predictions are found to be in good agreement with experiment. Influence of some of the governing parameters on the time development of the melting process is studied using the numerical simulation procedure.