Abstract: Storage tanks primarily refer to structures with liquid storage functions, such as storage vessels elevated water towers, and dams. Under seismic action, these structures exhibit significant fluid-structure interaction effects due to the bidirectional energy transfer between the fluid and the structure. The acoustic-structure coupling method is widely used for seismic response analysis of storage tanks, as it avoids the high computational complexity of computational fluid dynamics methods while maintaining good accuracy. This method introduces an additional fluid domain model, resulting in large-scale computational models. The interaction between the fluid and solid exhibits pronounced nonlinear characteristics. Using the traditional Newton-Raphson (N-R) iteration method for nonlinear analysis necessitates frequent updating and decomposition of the global stiffness matrix, significantly reducing the computational efficiency. Based on the fundamental theory of the inelasticity-separated finite element method, this paper considers the localized nonlinear characteristics of storage tanks. By introducing additional nonlinear degrees of freedom, the nonlinear relative displacement field of the element is established. The governing equations for the fluid-structure interaction interface elements within the IS-FEM framework are derived. A global computational model for the storage tank is assembled by integrating acoustic fluid elements, interface elements, and the existing inelasticity-separated solid elements. This leads to the proposal of a novel and efficient nonlinear analysis method for storage tanks. On this basis, an efficient seismic response analysis method for storage tanks is established. Since the method presented in this paper uses the Woodbury formula to solve for the displacement response of liquid-containing structures considering fluid-structure interaction, only a small-scale local nonlinear matrix needs to be updated and decomposed at each iteration step. This avoids the repeated updating and decomposition of the structure's global stiffness matrix, thereby enabling efficient simulation of the seismic response for such structures. Numerical examples verify the efficiency and effectiveness of the proposed method.