The present study explores numerically the processes of melting and solidification of a phase change material (PCM). The material used was a commercially available paraffin wax, which is non-toxic, recyclable, chemically inert, non-corrosive and can withstand an unlimited number of cycles. The phase-change material was stored in a rectangular box, open at the top. The bottom of the box could be heated or cooled. The inner space of the box was partitioned by vertical conducting plates attached to the bottom. Thus, heat was transferred to and from the PCM both through its melted/solidified layer and by conduction through the vertical plates. Transient two-dimensional numerical simulations were performed using the Fluent 6.0 software. The melting temperature of the wax, 23-25°C, was incorporated in the simulations along with its other properties, including the latent and sensible specific heat, thermal conductivity and density in solid and liquid states. The simulations provided detailed temperature and phase fields inside the system as functions of time, showing evolution of the heat transfer in the system as the phase change material melts/solidifies. The dependence of the heat transfer rate on the properties of the system and on the PCM phase composition at various time instants is presented and discussed.