A latent heat storage system has been designed to take advantage of the off-peak electrical energy for space heating. Using an enthalpy formation and a fully implicit finite difference method, the thermal performance of such a storage system with and without fins has been analysed. For the one-dimensional simulation model, calculations have been made for the melt fraction and energy stored for conduction plus convection and the conduction modes of heat transfer, while for the two-dimensional model, the same calculations have been made for conduction only. The magnitude of the melt fraction with fins is found to be considerable, dominating the melt fraction when no fin is used.