Because of their prominent advantages in strategic energy reserves and peacetime peak adjustment, underground salt cavern gas storages have drawn attention worldwide. Moreover, embedding wastes in the underground space of salt caverns complies with the global theme of ecological environmental protection. The creep properties of underground salt cavern gas storages directly impact the safety and stability of the long-term operation of gas storages. In this study, the physical model of the cavity in a selected gas storage was established based on the creep law and creep constitutive model of salt rocks. FLAC 3D software was adopted to simulate the rheological displacement and related plastic deformation of the surrounding rock under varying internal pressures. Safety indexes, such as the cavity volume shrinkage and safety factors of surrounding rocks, were calculated for different operating conditions. By controlling the cavity volume shrinkage, both the minimum and maximum operating internal pressure values were obtained. An optimized design scheme including optimized cavity shape and height-diameter ratio was proposed to ensure the long-term safe and stable operation of gas storages.