Abstract: Combining structural Finite Element Method (FEM),acoustic finite element and boundary element methods,a model of elastic shell vibration of an arbitrary shell-cavity structure coupled with internal and external sound fields is built.In addition,the transfer matrices from the excitation force to the vibration of the shell and the internal sound field are calculated.As the fluctuating pressure of Turbulent Boundary Layer (TBL) is a temporal-spatial random surface excitation,so the overall shape function matrix is introduced,and then the relationship between the power spectral density matrix of the generalized nodal force of the elastic shell and the power spectral density of the temporal-spatial random surface excitation is derived.Utilizing the vibro-acoustic coupled transfer matrix,relationships between the power spectral densities of vibration of the elastic shell/internal sound field and the power spectral density matrix of the generalized nodal force are obtained.Thus,the calculation method of vibration and internal sound field of an arbitrary shell-cavity structure induced by temporal-spatial random surface excitation is established.A typical vibro-acoustic coupled model of a rectangular cavity with acoustic media internally and externally,and with elastic rectangular plate on one side,is taken as example.The vibration of the elastic shell and power spectral density of the internal sound field are calculated and compared with the analytical method.The two results generally agree with the analytical one,with deviations of about 1 dB and 2 dB,respectively.The transfer matrix method has good adaptability which is not restricted by the shell-cavity structure and the shape of the inner region.