The present paper describes the simulation of phase change problems involving simultaneous multiple interface fronts employing the finite elements method. Much of the past investigations employing finite elements have been restricted to primarily a single phase change situation. The existence of more than one phase, that is, the presence of multiple phase fronts poses certain challenges and further complications. However, the results provide a very interesting thermal behavior for this class of problems. In this paper. attention is focused on fixed grid methods and the trapezoidal family of one-step methods using the enthalpy formulations. Illustrative examples which handle simultaneous multiple fronts in phase change problems are presented.