Salt rock is a sedimentary rock that is widely distributed in the crust. Since salt rock has a low permeability, rheological behavior, and self-healing characteristics, it has been extensively exploited for subsurface energy storage and waste disposal. The construction of compressed air energy storage (CAES) facilities using salt caverns for solution mining is a practical solution to achieve carbon peaking and carbon neutrality goals worldwide. The stability of the salt cavern surrounding rock is critical to the function of a CAES plant. Considering the triaxial stress condition of the rock surrounding such underground salt caverns, a number of triaxial creep-fatigue mechanics tests were performed on salt rock using an MTS815 mechanical testing device. The creep-fatigue damage to the salt rock was examined under various confining pressures and stress levels. The main research results and conclusions are as follows. First, the triaxial creep-fatigue stress-strain curves show a similar tendency to classical triaxial fatigue results: the strength and ultimate deformation of salt rocks increase as the confining pressure increases. Second, in contrast to typical fatigue test results, the residual strain before the highstress plateaus is larger than that after the plateaus during a creep-fatigue test. However, as the confining pressure increases, this disparity decreases. Third, fatigue loading increases creep deformation, and this effect weakens when the confining pressure increases. Fourth, the residual strain differential before and after the highstress plateau increases together with the stress level, and the contribution of creep strain increases correspondingly. Last, as the confining pressure increases, the salt rock behavior transitions from a brittle response to a fully ductile response. A high confining pressure prevents relative sliding between the salt rock particles. Thus, the effect of confining pressure on the creep-fatigue mechanical behavior of the salt rock reaches a threshold.