During the operation of gas storage wells, due to factors such as circulating casing pressure, poor cementation quality of cement sheath interface and poor mechanical properties, cement sheath produces plastic strain accumulation, fatigue damage, etc., which cause safety problems such as wellbore structure failure. In order to protect integrity of the wellbore, a three-dimensional finite element model of casing-cement sheath-formation composition is established considering cumulative plastic deformation and interface debonding behavior of the cement sheath during cyclic injection-production process, and the stress and cumulative plastic deformation of the cement sheath during cyclic injection-production process of the gas storage are discussed, and influencing factors are analyzed. The results show that the PEEQ of the CCI is larger than that of CFI, and the initial plastic strain is the highest and reaches 0.116, followed by a linear increase to 0.24. The effect of injection production load on radial and tangential stress is mainly related to the constraints of injection production load, formation, and cumulative damage, which leads to a decrease in material properties. When it is difficult to reduce the injection pressure, reducing the production pressure can also achieve the same effect of reducing PEEQ, with a difference of only 0.07%. Increasing elastic modulus, cohesion and friction angle of cement slurry and reducing Poisson's ratio can reduce risk of micro-cracks and interface damage in cement sheath. Intended to provide scientific basis for the safe operation and optimized management of gas storage facilities. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.