Abstract: The fluidstructure interaction vibration of stiffened structures is studied by using the method combining the finite element(FEM)with the boundary element(BEM).During the calculation, the damp stiffness of the structure is considered. A modified RITZ vector method and Newmark direct integral method are employed to overcome the difficulties of the numerical analysis caused by the unsymmetrical added mass.For numerical examples, the vibration and response of the composite cantilever plates and stiffened structures are analysed. Moreover, the effect of underwater explosion on a composite shiphull is liven.