Abstract:starting with the geometry characteristic of the cross section of eccentric cylindrical shell, the eccentric problem is converted into a circumferentially varying thickness problem. The vibration equations are written in a matrix differential equation by using the transfer matrix of the state vector of the shell. The natural frequencies of eccentric cylindrical shell are calculated and are compared to those of cylindrical shell. The main parameters which influence the natural frequency are analyzed, and the relationships between these parameters and the natural frequency are given. This paper not only proposed an effective new method to obtain the natural frequencies of an eccentric cylindrical shell, but also could be as a new idea and method for detecting the eccentricity of eccentric cylindrical shell.