The boundary element method was applied to simulate Stefan’s problem, and its results were compared with Neumanns’ solution. Temperature distributions and solidification thicknesses in solidification of iron, copper, and aluminum, calculated by the boundary element method, were in good agreement with the analytical solution. The proper time step in the boundary element method is closely related to geometrical data and thermal diffusivity, and it influences solution accuracy. It was found that the proper time step for transient heat conductions could be applied to simulate solidification problems involving phase change. The temperature recovery method was found to be a reasonable method to treat the latent heat of freezing during solidification in the boundary element method.