Nowadays, hydrogen is considered a potential successor to the current fossil-fuel-based energy. Within a few years, it will be an essential energy carrier, and an economy based on hydrogen will require appropriate hydrogen storage systems. Due to their large capacity, underground geological structures (deep aquifers, depleted hydrocarbon fields, salt caverns) are being considered for hydrogen storage. Their use for this purpose requires an understanding of geological and reservoir conditions, including an analysis of the preparation and operation of underground hydrogen storage. The results of hydrogen injection and withdrawal modeling in relation to the deep Lower Jurassic, saline aquifer of the Konary geological structure (trap) are presented in this paper. A geological model of the considered structure was built, allowable pressures were estimated, the time period of the initial hydrogen filling of the underground storage was determined and thirty cycles of underground storage operations (gas injection and withdrawal) were simulated. The simulations made it possible to determine the essential parameters affecting underground hydrogen storage operation: maximum flow rate of injected hydrogen, total capacity, working gas and cushion gas capacity. The best option for hydrogen storage is a two-year period of initial filling, using the least amount of cushion gas. Extracted water will pose a problem in relation to its disposal. The obtained results are essential for the analysis of underground hydrogen storage operations and affect the economic aspects of UHS in deep aquifers.