Thermal storage has been considered as an important measure to extend the operation of a concentrated solar power plant by providing more electricity and meeting the peak demand of power in the time period from dusk to late night everyday, or even providing power on cloudy days. Discussed in this paper is thermal energy storage in a thermocline tank having a solid filler material. To provide more knowledge for designing and operating of such a thermocline storage system, this paper firstly presents the application of method of characteristics for numerically predicting the heat charging and discharging process in a packed bed thermocline storage tank. Nondimensional analysis of governing equations and numerical solution schemes using the method of characteristics were presented. The numerical method proved to be very efficient, accurate; required minimal computations; and proved versatile in simulating various operational conditions for which analytical methods cannot always provide solutions. Available analytical solutions under simple boundary and initial conditions were used to validate the numerical modeling and computation. A validation of the modeling by comparing the simulation results to experimental test data from literature also confirmed the effectiveness of the model and the related numerical solution method. Finally, design procedures using the numerical modeling tool were discussed and other issues related to operation of a thermocline storage system were also studied.