Gas storage facilities are crucial for ensuring national energy security and stabilizing supply during peak-demand periods. However, during operation, gas storage facilities are prone to risks such as fault reactivation and local caprock breakthrough, potentially leading to gas leakage. Therefore, it is necessary to analyze their mechanical integrity. To clarify the stress variation patterns of the gas storage X and enhance the upper limit of the operational pressure and overall storage efficiency, this study integrated geological, seismic, logging, production, and laboratory data to establish one-dimensional and three-dimensional geomechanical models of the gas storage X. Based on production history matching and cyclic gas injection and production patterns, a four-dimensional dynamic geomechanical model was established. The stress variation patterns and mechanical integrity of the caprock, reservoir, base support layer, and faults during the injection and production process were analyzed. The injection-production plans were optimized by considering deliverability and mechanical integrity. The results showed that: (1) The Longtan Formation caprock of the gas storage X was characterized by a relatively low Young’s modulus, high Poisson’s ratio, and weak mechanical strength. The more argillaceous the lithology, the lower the modulus and the smaller the horizontal stress. (2) The initial in-situ stress state of the caprock corresponded to a strike-slip faulting regime, while the reservoir corresponded to a reverse faulting stress regime. (3) During the injection-production process of the gas storage X, the caprock and base support layer experienced minimal stress variation and posed low failure risk. (4) The pore pressure of the reservoir changed significantly, and the pressure variation was greater than stress changes. (5) During the injection-production process, the risk of matrix failure in the reservoir was low, but the failure risk increased in the main injection-production area after gas injection. There was a slip risk when the bottom hole pressure exceeded the original gas reservoir pressure by about 3 MPa. (6) Under the condition of ensuring the mechanical integrity of the gas storage X, the optimized injection-production plan yielded an approximately 34% increase in cumulative gas injection compared to pre-optimization. The results provide theoretical and methodological support for in-situ stress analysis and mechanical integrity evaluation of the gas storage X.