In order to ensure the national demand for peak shaving and supply guarantee, the project of Xiangguosi underground gas storage capacity expansion for target productivity has been proposed and being carried out. For the purpose of effectively guiding the optimization of the operation upper limit pressure of the gas storage and ensuring its long-term safe operation, it is urgently needed to carry out the assessment of the integrity of the cap rock of the gas storage and the stability of its faults. Based on geological, seismic, logging, dynamic monitoring data and core experimental data, this paper established static and dynamic geomechanical models of the gas storage and analyzed the characteristics of the in-situ stress of different layers of it to simulate and evaluate the stability of the cap rock, underpinning layer and faults of reservoir under different pore pressure. The results showed that 5 reservoir-controlling faults had no risk of fault activation in the early operation of the gas storage and the current stress conditions, with good sealing performance, and when the reservoir pressure was 6MPa higher than the original formation pressure, there was a risk of instability in the integrity of the gas storage. The research results finely and quantitatively evaluated the operation safety of the gas storage under the influence of the dynamic stress field, and had important guiding significance for the optimization of the operation plan of the gas storage.