This paper presents a numerical and theoretical analysis of thermal wave propagation in packed bed thermal reservoirs for energy storage applications. In such reservoirs, the range of temperatures encountered is usually such that the solid storage medium will exhibit significant changes in specific heat capacity. This in turn results in non-linear wave propagation and may lead to the formation of shock-like thermal fronts. Such effects have an impact on the exergetic losses due to irreversible heat transfer, and should be taken into account during the design and optimisation of the reservoirs. In the present paper, the emphasis is on thermal losses due to irreversible heat transfer. Frictional (pressure) losses and heat leakage between the storage medium and the environment are also important but are not considered here. The implications of the results for storage material, and particle size are discussed briefly in the context of loss minimisation.