Underground energy storage is an important function of all energy supply systems, and especially concerning the seemingly eternal imbalance between production and demand. Salt rock underground energy storage, for one, is widely applied in both traditional and renewable energy fields; and this particular technique can be used to store natural gas, hydrogen, and compressed air. However, resource diversification and structural complexity make the supply system increasingly uncertain with the passing years, leading to great challenges for energy storage facilities in the present, and perhaps going into the future as well. Hence, it is necessary to research the operation stability of underground energy storage further. In this paper, a stability evaluation index system of Underground Gas Storage (UGS) is constructed with natural gas as the main medium, according to FLAC 3D cavity creep simulation software, along with fuzzy membership function to comprehensively determine the impact factor scoring model; the subjective weight is calculated based on the improved Analytic Hierarchy Process (AHP), the objective weight is calculated by the Entropy Weight Method (EWM), the combined constant weight is obtained by combining the variance maximization theory, and introducing the variable weight theory to obtain a more accurate combined variable weight. Finally, with this all being considered and accounted for, and with the four different conditions designed for UGS deployment case analysis and verification taken into consideration, the combined variable weight evaluation achieved excellent results; compared with the traditional constant weight method, in fact, the new evaluation results are more rigorous and objective.