The solidification of the phase-change material within a finned heat pipe latent heat thermal storage system is studied by means of an analytical technique considering the radial heat propagation toward the heat pipe wall and the angular propagation toward the fin. Two approximations for the temperature profile along the fin height are used: a parabolic approximation (method I) and an exponential one (method II). The position of the solid-liquid interface is plotted according to the two methods for different fin numbers and the results are compared and discussed.