This research concerns the alternate melting and freezing of a phase change material (PCM) to simulate cyclic operation of phase change energy storage systems. A one-dimensional conduction-controlled phase change model was derived for a PCM slab. One surface of the slab is subjected to successive periods of constant temperature above and below the fusion temperature while the other surface is adiabatic. A front-tracking, self-marching finite-difference scheme was developed to solve the resulting multiple moving boundary problem. Temperature fields within each solid and liquid region were decoupled with an explicit treatment of the interfacial energy balances. Temperatures at all grid points were obtained by an explicit finite-difference scheme except for the grid points in the immediate neighborhood of each phase front. Temperatures at the latter points were computed from a quadratic temperature profile with time-dependent coefficients. Dynamic simulations were carried out until a periodic steady state was attained when the energy stored during a melting period and the energy recovered in the following freezing period were equal and remained invariant for subsequent periods. The cumulative energy transferred, the instantaneous heat flux, the interface locations and the temperature profiles were obtained for three modes of operation: (1) equal thermal swings with equal melting and freezing periods, (2) equal periods with unequal swings and (3) equal swings with unequal periods. Experiments were carried out by alternately melting and freezing n-octadecane in a thin rectangular cell. When the cell was horizontal and heat was transferred from above, the moving interfaces were planar and there was excellent agreement between numerical and experimental results. When the cell was tilted, the interfaces were not planar and the energy transferred at the periodic steady state increased with the angle of inclination, reaching a maximum with heat transfer from below.