The long‐term cyclic gas injection and production mode of the gas storage will lead to accelerated deformation of the surrounding rock of the old cavity, and even the instability and failure of the cavity. Considering the geological conditions and cavity measurement data of the old cavity of the horizontal butted‐well in China, the deformation and failure characteristics of the long‐term cyclic injection‐production process of the surrounding rock of the old cavity under different internal pressure difference and injection‐production frequency are studied. The long‐term stability of the gas storage is predicted by six indexes: the deformation of surrounding rock, dilatancy safety factor, volume shrinkage rate, plastic zone volume, equivalent strain, and no tensile stress. The results show that with the increase of operation duration and cycle times, the deformation, volume shrinkage rate, and plastic zone volume of the surrounding rock gradually increase after the old cavity is reconstructed into the gas storage and the difference of results under different UGS and CAES gradually expands. The stability of the surrounding rock of the old cavity under the cycle action of CAES will be lower. The number of cycles has a limited impact on the stability of the surrounding rock of the old cavity, while the operation duration and injection‐production pressure are the main determinants of the stability of the surrounding rock of the old cavity. If the old cavity of the salt mine is reconstructed into CAES, the parameters such as the number of cycles, the operation duration, and the injection‐production pressure still need to be considered comprehensively. The research results can provide reference value for the reasonable design of the gas storage pressure range of the old cavity and the safety and stability evaluation of the surrounding rock.