Melting of a pure phase change material (PCM) in a rectangular container heated from below is simulated using the Streamline Upwind/Petrov Galerkin finite element method in combination with a fixed grid primitive variable method. boussinesq assumption is invoked and two-dimensionality is assumed. flow patterns for a wide range of Rayleigh numbers are presented. Instability of free convection flow during the melting process is discovered and discussed.