Abstract: The effect of multiple compliant layers on the sound radiation from a finite cylindrical shell immersed in an infinite acoustic medium is studied.The transfer matrix is derived according to the continuous boundary conditions on each adjacent interface of the multi-layer system.With the shell theory and the acoustic wave equation,the theoretical model is developed to estimate the characteristic of sound radiation.The numerical calculation results show that the amount of the acoustic radiation power reduction increases as the wave speed or the density of the compliant layer decreases,and using multi-layer system could be more effective on the noise reduction than the corresponding uniform single layer.