In this paper,we are conceed with the coupling of finite element methods and boundary integral equation methods solving the classical fluid-solid interaction problem in two dimensions.The original transmission problem is reduced to an equivalent nonlocal boundary value problem via introducing a Dirichlet-to-Neumann mapping by the direct boundary integral equation method.We show the existence and uniqueness of the solution for the corresponding variational equation.Numerical results based on the finite element method coupled with the standard Galerkin boundary element method,the fast multipole method and the Nystr(o)m method for approximating the DtN mapping are provided to illustrate the efficiency and accuracy of the numerical schemes.