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We are concerned with numerical solutions for the interaction problem of plane acoustic waves in a compressible,inviscid fluid with an elastic structure.The mathematical model can be formulated by a coupling system of the time-harmonic Navier equation in the elastic domain and the Helmholtz equation in the fluid region with appropriate transmission conditions at the interface.We investigate numerical solutions of the problem based on finite element method and boundary integral equation methods.Essential theoretical analysis for numerical models and numerical solutions will be discussed.