To increase natural gas storage capacity and further utilize salt mine resources, salt cavern gas storage in the Yunying salt mine, Hubei Province, China, was simultaneously constructed in two different mining layers (K3 and K4). The purpose of this study was to investigate the long-term feasibility of operating salt caverns for gas storage in two mining layers. Based on the geological conditions and sonar test results, the geometric parameters for the salt caverns in the two mining layers were designed, and a 3D geomechanical model was built to predict the cavern stability. The corresponding evaluation index included the displacement, volume shrinkage rate, equivalent strain, and dilatancy factor. The results show that simultaneously operating salt cavern gas storage in two mining layers is feasible, and the operational pressures for the salt caverns in mining layers K3 and K4 should be no less than 4–9 and 7–12 MPa, respectively, to satisfy the stability requirements. The surrounding rock of the salt caverns presents a larger displacement and volume reduction compared with cases in which the salt caverns are operated in a single mining layer. Increasing the injection–withdrawal frequency increases the deformation of the surrounding rock.