Abstract: In this paper, thewave propagation characteristics of infinite cylindrical shells withcircumferential surface crack are investigated. The vibration of thecylindrical shell is described by Fl\"ugge's shell equations and the wavepropagation approach is used to solve the equations. Inconsideration of the crack's three modes: opening, sliding and tearingmodes andtheir combinations, the surface crack is modeled by distributed line springs.The local compliance matrix at the cracked region is then deduced by usinglinear elastic fracture mechanics, and the relationships between theadditional general displacements and the general forces are obtained. To verify the accuracy of the theoretical model and the wavepropagation method proposed, the axisymmetric free vibration of a finiteshell with a circumferential surface crack is investigated first, thenatural frequencies of the finite cracked shell are calculated by usingtheanalytical method and finite element method, respectively. The resultsbetween the two methods show a good agreement. Then an infinite shell with acircumferential surface crack is investigated. For a given incident wave,the amplitudes of the reflected wave and transmitted wave are obtainedaccording to the continuity conditions of displacements and inner forcesat both sides of the crack. The relationships between the transmitted wavecoefficient and the crack's depth as well as the frequency areobtained. The numerical results indicate that the existence of the crackchanges the vibration wave in the shell substantially and the amplitudes ofthe transmitted wave and reflected wave are closely related to the crack'sdepth and the frequency. The results also show that the coefficients ofthe transmitted wave decrease with the increase of the crack's depth. Thisresearch provides a theoretical basis for the further crack detection incylindrical shells based on the vibration method.