The multi-layer gas cylinder is made up of an outer SF6 gas ring and an inner air cylinder. The scenarios of various shock Mach numbers (M = 1.27, 1.5, 1.7, and 2.1) are investigated by the numerical simulation based on a multi-block parallel finite-volume CFD code. The intense Mach numbers result in stronger compression on the outer interface. A large amount of baroclinic vorticity is deposited at the interface, inducing the generation of vortex pairs. In addition, a jet can be observed at the vicinity of the upstream pole of the outer interface, which penetrates the surrounding gas at higher Mach numbers. As the shock Mach number increases, the widths of both gas cylinders decrease during the early phase of the evolution under the effect of intense compressibility, while the heights of both cylinders are promoted afterward due to the development of the primary vortex pair. For the mixing of various gases, a numerical simulation of the circulation is conducted in this study, which implies that an intense shock wave can promote the deposition of vorticity on both interfaces of outer and inner cylinders, enhancing the development of vortex pairs and accelerating the mixing of SF6 and air.