Abstract Solution-mined caverns excavated in rock salt formations are recognized as the appropriate places for underground storage of energy in the form of compressed air and hydrogen. These caverns are subjected to different loading conditions during the construction and operation time. Therefore, it is essential to investigate the mechanical response of rock salt for all life stages of the cavern such as leaching phase, debrining process, first filling as well as cyclic loading operation. To achieve this goal, proper constitutive laws are required to describe the material behavior of rock salt at different time scales. In this paper, an elasto-viscoplastic-creep model is employed to predict the stress-strain relation around the cavern during the construction and cyclic operation phases. The proposed creep law is a modified version of Norton creep law which accounts for the time-dependent volumetric deformation. Additionally, a damage parameter which is dependent on the released inelastic work is included in the model to predict the material failure. To accomplish this, first, the material parameters of the employed model are determined using the relevant experimental data available in the literature. Then, the excavation process and cyclic loading operation of a typical salt cavern are numerically simulated. The stress paths around the cavern as well as the volume convergence, damage propagation and permeability changes are evaluated considering two loading scenarios, and finally, the allowable operating conditions for the simulated cavern are identified.