The concept of a solar energy heat pipe latent heat storage system is presented. In order to assure large charging and discharging rates, finned heat pipes are used to transfer heat to and from the phase-change material (paraffin in this case). The evolution of the solid - liquid interface is studied by considering the radial heat transfer (due to the heat pipe wall) and the angular one (due to the fin). Two mathematical models, corresponding to exponential, respectively polynomial functions describing the fin temperature profile are presented and the results are compared. The two models allow the evaluation of the discharge time of the storage unit for a certain number of fins for a single heat pipe. When the discharge time has a fixed value, the methods presented in the paper allow to conclude whether the number of fins is sufficiently large to assure the complete solidification of the phase-change material.