Abstract: In most practical engineering projects on fluid-solid interaction, the deformation of thin elastic component is geometrically nonlinear, and the equations for fluid are also nonlinear, hence there exist strong nonlinearity on the interface between the fluid and the elastic body. The equations and contact conditions are established by combining Lagrangian and Eulerian methods on the interface. There exist four approaches: single Lagrangian method, single Eulerian method, compatible Lagrangian-Eulerian method and arbitrary Lagrangian-Eulerian method. The fluid-solid interaction can be classified through 、 for describing the characteristics of elastic deformation and for expressing the trait of flow. Based on theory of fluid elastic mechanics, the description method for fluid-solid interaction is presented, and the corresponding classification method is established from the perspective of geometrical nonlinearity using the non-linear elasticity theory by V.V. Novojilov. The simplification for contact condition, kinematic condition and dynamic condition on the interface is credible.