Rock salt is considered as a potential medium for energy storage，nuclear waste deposit for its excellent creep，low permeability and damage recovery behaviors. Based on laboratory creep test results of rock salt，nonlinear creep constitutive model and damage evolution equation are suggested. The developed constitutive model and damage evolution equation are programmed by FEM；and comparison between laboratory data and numerical results are given. Furthermore，the numerical code is applied to the simulation of creep and damage behaviors of underground salt caverns during natural gas injection and pumping. The creep damage evolution zones of the caverns are obtained from the numerical analysis. The achievements from the research work can provide references to the design of Jintan Underground Gas Storage.