Abstract: An equivalent thin-walled circular pipe model is used to analyze torsional natural frequency of U-shaped bellows. The equivalent radius and the torsional stiffness of U-shaped bellows are defined. Two methods are used to calculate the equivalent radius. Torsional stiffness of U-shaped bellows is calculated using Chien's integration formula for torsional stiffness of revolutionary shells and the equivalent circular pipe model, respectively. The corresponding calculation methods for torsional natural frequency of U-shaped bellows are called integrated method and simplified method, respectively. Finite element analysis is performed to verify the results from the two methods, and good agreement is reached between them. The results from the integrated method are found more accurate, while the simplified method is more suitable for engineering calculation.