A numerical study of transient natural convection heat transfer from a finned surface has been conducted for thermal storage in an enclosure. The motivation of this work is found in solar thermal storage tanks. The finned heat exchanging surface provides a means to charge and discharge the thermal energy in the tank. The governing time-dependent conservation equations are solved by a finite difference method. Solutions are obtained for 106< Ra < 108, for 0-3 fins, for fins of length L/H = 0.3 and 0.75, and for fins parallel and perpendicular to the gravity vector. Results indicate that the storage process is characterized by three distinct heat transfer regimes and that most of the energy is stored during the last regime, referred to as the decay period. The time-changing Nussett number at the heat exchanging surface is strongly dependent on the Rayleigh number and the number of fins. It is, however, much less sensitive to the size of the fins and their orientation. The storage times are shortened as Ra increases and/or the number of fins and/or their size increases.