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Compressed Air Energy Storage (CAES) is a commercial, utility-scale technology that is suitable for providing long-duration energy storage. Underground air storage caverns are an important part of CAES. In this paper, an analytical solution for calculating air leakage and energy loss within underground caverns were proposed. Using the proposed solution, the air leakage and energy loss under a typical CAES operation pressure were analyzed, and the influences of the permeability of the concrete lining and the lining thickness on the sealing efficiency of underground caverns were investigated. The results showed that under a typical CAES operation pressure, a concrete lining with a permeability of less than 6.36 × 10−18 m2 would result in an acceptable air leakage rate of less than 1%. Air leakage will increase linearly with increasing lining permeability. Increasing the thickness of the concrete lining could enhance the sealing efficiency of the storage cavern.