In this paper, the finite element method (FEM) and the boundary element method (BEM) are combined together to solve a class of fluid-structure interaction problems. The FEM is used to model the elastic structure and the BEM is used to model the acoustic fluid. Quadratic isoparametric elements are used in both the FEM and BEM models. Continuity conditions of pressure and normal velocity are enforced at the fluid-structure interface on which the normal vector is not required to be uniquely defined. An enhanced CHIEF formulation is adopted to overcome the nonuniqueness difficulty at critical frequencies. To reduce the dimension of the coupled structural acoustic equations, the structural displacement is approximated by a linear combination of either Ritz vectors or eigenvectors. An error norm and a participation factor are defined so that it is possible to evaluate the accuracy of a solution and to omit vectors with small participation factors. Example problems are solved to examine the accuracy of the numerical solutions and to compare the efficiency of the Ritz vector and eigenvector syntheses.