With the worldwide demand for electricity, renewable energy is attracting increasing attention. As this energy has an intermittent character, large-scale storage technologies are necessary. One of the most promising systems is the advanced adiabatic compressed air energy storage (AA-CAES) in underground lined rock caverns. The high cyclic thermal and mechanical loadings involved in the system can disturb the surrounding geological barrier and thus lead to the failure of the system. The implementation of a special lining capable of limiting the thermal losses, reducing the air leakage and ensuring the caverns stability, is therefore required. This paper presents the governing equations for fully coupled thermo-hydro-mechanical (THM) processes in saturated deformable media filled with dry air which characterize the conditions of the storing system. The assumptions used to simplify the equations are discussed and the neglected terms are underlined. These equations take into account the dependence of thermal conductivity on temperature, convection and heat compression. The air properties are derived using Helmholtz energy. A comprehensive comparison between the proposed model and a simple THM model based on constant parameters, ideal gas and conductive flux is made in order to emphasize the phenomena that could occur and their influences. Finally, thermo-hydro-mechanical simulations of the different lining materials are carried out to analyze the advantages and the drawbacks of each solution.