Abstract: The coupled vibration characteristics of liquid and a flexural annular baffle in a cylindrical rigid tank were studied. The complicated fluid domain is separated into four simple sub-domains composed of two circular columns and two annular columns, respectively. The velocity potential functions corresponding to every fluid sub-domain were analytically solved by using the separation variable method and the decomposition method. The dry-modal functions were used to expand the wet modes in order to solve the differential equation of coupled vibration of the baffle and liquid. Based on the consistent conditions of liquid movement between the sub-domain interfaces and the surface wave equation of fluid, the unknown coefficients in the solutions were determined by using the Fourier series expansions and the Bessel series expansions. Finally, the eigenvalue equation was obtained. The coupled frequencies were numerically calculated by using the searching root method for non-linear equations. The convergence study shows high accuracy of the present method. The numerical results were compared with those obtained from the ADINA finite element software. An excellent agreement has been achieved.