In this paper the thermal behavior of a phase change material element bounded by a fluid whose temperature varies periodically in time, is examined. Two cases have been envisaged, those of the plate and the hollow cylinder. The numerical method proposed, allows one to solve the multi-boundary problems. In a way very similar to the case of sensible heat storage, it is established that for a given material and for a fixed time it exits an optimal thickness for which the stored energy per unit of exchange surface is maximum. It is remarked that a cylindrical form, in particular for small inner radii, is slightly less suitable than the plane configuration. In all the situations envisaged in this study, it has never been observed more than two simultaneous boundaries. Further it is shown that the optimal thickness corresponds to one case of total melting of the storage. © 1979.