Abstract: The membrane theory is widely used in analyzing vibrations of thin-walled cylindrical tubes.Here we use the shell theory of elasticity to analyze the radial-longitudinal coupled vibration of finited thin-walled elastic cylindrical tubes in this paper.Vibration equations and general solutions as well as the eigenfrequency equations under different boundary conditions are studied.Analytic and calculated results showed that the shell theory can not only give more perfect explanation in analysis,but also give more perfect results in calculation