Fluctuations in renewable energy production, especially from solar and wind plants, can be solved by large-scale energy storage. One of the possibilities is storing energy in the form of hydrogen or methane−hydrogen blends. A viable alternative for storing hydrogen in salt caverns is Lined Rock Cavern (LRC) underground energy storage. One of the most significant challenges in LRC for hydrogen storage is sealing liners, which need to have satisfactory sealing and mechanical properties. An experimental study of hydrogen permeability of different kinds of polymers was conducted, followed by modeling of hydrogen permeability of these materials with different additives (graphite, halloysite and fly ash). Fillers in polymers can have an impact on the hydrogen permeability ratio and reduce the amount of polymer required to make a sealing liner in the reservoir. Results of this study show that hydrogen permeability coefficients of polymers and estimated hydrogen leakage through these materials are similar to the results of salt rock after the salt creep process. During 60 days of hydrogen storage in a tank of 1000 m2 inner surface, 1 cm thick sealing liner and gas pressure of 1.0 MPa, only approx. 1 m3 STP of hydrogen will diffuse from the reservoir. The study also carries out the modeling of the hydrogen permeability of materials, using the Maxwell model. The difference between experimental and model results is up to 17%, compared to the differences exceeding 30% in some other studies.