A simple, robust and reliable explicit numerical method MAC (Marker and Cell) is applied for melting of gallium by fixed-grid method on an unstructured grid. Owing to no limitation on the time step for implicit method, this investigation also apply implicit MAC method for the same problem. Results obtained from the unstructured triangular grid correlate well with the structured mesh computations and experimental data. Also, the feasibility of applying the triangular grid to the complex geometry is demonstrated by calculating triangular domains for a transient melting process. Results presented herein give further insight into the melting of pure metal problem.