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Underground hydrogen gas storage (UHS) at depleted hydrocarbon reservoirs may balance energy production/ consumption during seasons by utilizing the capability of hydrogen gas. The geomechanical behavior of the reservoir rock during UHS operation cycles is an effective parameter of the overall quality and quantity of this operation. This study investigated the impact of rock geomechanical behavior on the quality and quantity of UHS operation performance in a depleted oil reservoir. Three geomechanical behaviors, namely, elastic deformation, irreversible compaction of rock, and dilation−recompaction, form the basis of this study. We numerically investigated how these cases affect wellbore injectability, hydrogen recovery, production of in situ reservoir fluids, and the number of hydrogen injection/production wells. Based on the results of this study, the performance of wells during the injection of hydrogen in the dilation case was better than in other cases. After 10 cycles, 87% of the designed cumulative volume of hydrogen was injected into the reservoir. Though the irreversible compaction case injected the least cumulative hydrogen, it generated the highest hydrogen recovery during annual cycles and at the end of UHS operation (93%). The production of nonhydrogen fluids is known as a problem in UHS operations in depleted hydrocarbon reservoirs. After 10 cycles of hydrogen injection and production and 3 years of prolonged production, the dilation case produced less water and oil overall than other cases. Also, fewer wells are required to achieve the designed injection amount in the dilation case compared to base and irreversible compaction cases. Therefore, the costs associated with hydrogen injection and production wells in reservoirs with geomechanical dilation behavior are lower.