Energy production from renewable energy sources is not stable and any fluctuations in energy productions need to be eliminated with underground energy storage. Demand of underground gas storage will be increasing, due to the switching to green energy, while the availability of underground storage sites, especially salt caverns suitable for hydrogen storage, is limited. The purpose of this paper is to compare the hydrogen permeability of different materials and select a proper liner material for hydrogen storage in Liner Rock Caverns or post mine workings. A variety of materials, like concrete, polymer concrete, epoxy resin, salt rock, and mudstone, were tested for gas permeability/hydrogen diffusion, using the combined Steady-State Flow/Carrier Gas methods. Results are shown in different units, providing the opportunity to compare the results with literature data. The permeability value of investigated epoxy resin is comparable to the salt rock (after creep process), which makes the epoxy resin a promising sealing liner for hydrogen and potential substitution of stainless-steel in Lined Rock Cavern (LRC) gas storage.