Underground compressed air energy storage chambers are a promising emerging energy storage technology with strict limitations relating to the stability of the surrounding rock. This study conducted displacement and plastic zone analyses during the excavation and stabilization phases of the chamber utilizing the finite difference method based on engineering data, demonstrating that the stability of salt rock can effectively withstand internal pressures ranging from 0 to 9 MPa, with an average of 15 mm in the Z-axis and 19.23 mm in the X-axis. To further investigate the feasibility of subterranean energy storage reservoirs, the FOS for various surrounding rocks was calculated at different burial depths. These results facilitated a parameter sensitivity analysis on the stability of the surrounding rock of the underground energy storage reservoir. The dynamic reaction of the underground chamber was studied using synthetic seismic wave technology, demonstrating that the seismic capacity of the structure adhered to the code, and the post-seismic displacement remained within the safe range (Z-axis 34 mm, horizontal 19 mm). The results demonstrate the stability analysis method of the chamber and establish a foundation for the extensive implementation of CAES which will contribute to the development of energy storage technology.