Solid sensible heat storage is an attractive option for high-temperature storage applications in terms of the investment and maintenance costs. Typical solid thermal energy storage systems use a heat transfer fluid to deposit and extract heat as the fluid flows through a tubular heat exchanger embedded in the solid storage material. A one-dimensional unsteady model of the heat transfer and energy storage in a solid heat storage module was developed using a modified lumped capacitance method which is valid for large Biot numbers with the introduction of an effective heat transfer coefficient. Experiments using water as the heat transfer fluid and concrete as the storage material were used to validate the model. The model was used to analyze a cylindrical energy storage unit to study the energy storage in the storage module and optimize the design.