Parabolic trough power systems utilizing concentrated solar energy have proven their worth as a means for generating electricity. However, one major aspect preventing the technologies widespread acceptance is the deliverability of energy beyond a narrow window during peak hours of the sun. Thermal storage is a viable option to enhance the dispatchability of the solar energy and an economically feasible option is a thermocline storage system with a low-cost filler material. Utilization of thermocline storage facilities have been studied in the past and this paper hopes to expand upon that knowledge. The heat transfer between the heat transfer fluid and filler materials are governed by two conservation of energy equations, often referred as Schumann  equations. We solve these two coupled partial differential equations using Laplace transformation. The initial temperature distribution can be constant, linear or exponential. This flexibility allows us to apply the model to simulate unlimited charging and discharging cycles, similar to a day-today operation. The analytical model is used to investigate charging and discharging processes, and energy storage capacity. In an earlier paper , the authors presented numerical solution of the Schumann equations using method of characteristics. Comparison between analytical and numerical results shows that they are in very good agreement.