Based on the classical shell and ideal potential flow theory, the motion equation of the fluidstructure coupling system of the coaxial cylindrical shell is established, and the finite difference method (FDM) is introduced to discretize the motion equation. An expansion method applying the piecewise function as the basis function is proposed in this paper. A fluidstructure coupling solution strategy of a coaxial cylindrical shell based on FDM is developed. We apply this method first to solve the vibration frequency of the coaxial cylindrical shell in a static fluid and compare it with the ANSYS to verify the correctness of this method. Then, the influence of structural parameters of coaxial cylindrical shell on its vibration frequency in hydrostatic is explored; Finally, the hydraulicelastic instability of the coaxial cylindrical shell system is studied.