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In this paper, the numerical calculation model of salt cavern hydrogen storage was established based on the proposed salt cavern hydrogen storage in a bedded salt mine in Jiangsu Province of China. The effects of the minimum internal pressure, maximum internal pressure, average internal pressure and injection-production rate on the stability and tightness of the storage were explored respectively. The results revealed that: (1) The volume shrinkage rate and the plastic zone distribution of the surrounding rock decreased with the increase of the minimum internal pressure, and increased with the decrease of the maximum internal pressure. (2) When the depth of salt cavern is around 1700 m , its long-term stability cannot meet the requirements according to the traditional standard of 0.3–0.8 times of the vertical stress at the cavern roof. It is therefore suggested that the minimum internal pressure of the storage should be increased to 0.4 times of the vertical stress at the cavern roof. (3) The tightness evaluation indexes, including leak range, pore pressure distribution of hydrogen, and cumulative leakage of hydrogen in surrounding rock, all increased with the increase of average pressure and amplitude of internal pressure. (4) Under the same average internal pressure and injection-production frequency, the greater the injection-production rate (the amplitude of internal pressure), the smaller the cumulative leakage rate is. Therefore, increasing the injection-production rate is beneficial to the storability of the hydrogen storage. • Different internal pressures are set to study the stability and tightness of the salt cavern for hydrogen storage. • Raising the minimum internal pressure can enhance the stability of the salt cavern. • The amplitude of internal pressure is the key factor affecting the tightness of the salt cavern. • The selection of internal pressure for hydrogen storage should take into account the effects of multiple factors. [ABSTRACT FROM AUTHOR]