It is well known that increasing the damping of machinery structures will reduce noise radiation due to ringing vibration. Damping in industrial pipes can be increased by various damping techniques. This study was motivated by the need to decrease the noise radiation and vibration of pipework in power plants, particularly at elevated temperatures. Based upon the physical phenomenon of the air film damping of two parallel plates, a double pipe damping system with a very small air gap was investigated. In analysis, the Flugge shell equations of motion and the Navier-Stokes equation for viscous fluid were employed. First, a traveling wave-type solution was taken for shell and fluid. Then, from the interface conditions between the shell and fluid, the solution for the fluid medium was expressed in terms of shell displacements. Finally, solving the fluid equation of motion gave the fluid velocity profiles and stresses in the clearance between two cylindrical shells. From the definition of energy dissipated in the fluid, the equation of loss factor of the whole system was derived. The analytical results showed a very good qualitative agreement with the experiment. The study showed that different shell modes had a different contribution to the squeezing film damping, and the optimal design of the double pipe damping system can be deduced. The theory has been extended to studying the squeezing film damping system with various kinds of viscous fluid, such as lubrication oil, etc.