Energy storage cells with phase change offer a possibility of better utilization of waste and solar thermal energy. This paper presents the results of an analysis of this type of cells, for the energy storage process (charging), and the release of energy process (discharging). The analysis considers two cases, (i) a process in which the phase change material melts from the bottom of the cell under which a constant temperature source is maintained, and (ii) a process in which the melting occurs by heating the cell with a fluid flowing under the cell. The results include the evolution of the solid-liquid interface, and the determination of how much energy has been stored throughout the whole process.