The deep understanding of the dynamic stress evolution law and influencing factors of the cap rock under the multi-cycle injection-production cycle is helpful to scientifically and effectively predict the setting of the upper limit pressure in the process of gas reservoir injection and production. According to the operation mechanism of the gas storage injection and production and the rock mechanics theory, the formation deformation and pore pressure change are the main factors affecting the disturbance of the cap rock stress field, that is, the change of the stress field of the gas reservoir cap rock is caused by the deformation of the reservoir and the change of the cap rock seepage field. The size of the influence of the reservoir is not accurately evaluated in the traditional cap rock stress analysis theory. In order to supplement the above theory, this study takes the S gas reservoir in Songliao Plain as the research object, and conducts corresponding research on the cap rock through different working conditions. Based on the rock fluid-solid coupling theory, the supracrustal rock is regarded as a porous medium, and the geological mechanics model that considers the cap rock, reservoir and the bottom layer is established. The above two factors are numerically simulated by ignoring the deformation effect of the reservoir, the impermeability of the cap rock and the actual formation conditions. Meanwhile, the gas storage full life cycle (three stages as gas reservoir depletion, injection and multi-cycle injection and production) is taken into account as well. The research results show that the change of the seepage field of the cap rock has the most significant effect on the stress field of the cap rock, and the most sensitive part of the stress change is located at the junction of the cap rock and the reservoir. This research not only has important practical significance, but also has important scientific research value. It will enrich the evaluation theory of gas storage cap rock sealing and provide reference for engineering practice.