- Theoretically speaking, it is impossible to make the differential equation of motion uncoupled for the natural modes of a system in consideration of the attached water. The hydro-elastic structure is equal to the, non-proportional damping system. In this paper a perturbation analysis method is put forward. The structure motion equation is strictly solved mathematically, and the non-proportional damping problem is transformed into a series of proportional damping ones in the superposition form. The paper also presents the calculation formula of the dyanamic response of the structure being subjected to harmonic and arbitrary load. The convergence of the proposed method is also studied in this paper, and the corresponding convergence conditions are given. Finally, the proposed method is used to analyze the displacement response of a real offshore platform. The calculation results show that this method has the characteristics of high accuracy and fast convergence. - Theoretically speaking, it is impossible to make the differential equations of motion uncoupled for the natural modes of a system in consideration of the attached water. The hydro-elastic structure is equal to the, non-proportional damping system. In this paper a perturbation The structure motion equation is strictly solved mathematically, and the non-proportional damping problem is transformed into a series of proportional damping ones in the superposition form. The paper also presents the calculation formula of the dyanamic response of the structure The subjected of the harmonic method is also studied in this paper, and the corresponding convergence conditions are given. Finally, the proposed method is used to analyze the displacement response of a real offshore platform. The calculation results show that this method has the characteristics of high accuracy and fast convergence.