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A boundary element method has been developed to calculate the added mass matrix of fluid coupled structures in the case when the fluid is assumed to be compressible and inviscid. The potential flow is represented by a double layer density with linear interpolation functions. A linear set of equations for the fluid motion is obtained by Galerkin's procedure. The added mass matrix is not symmetric but a symmetrization procedure is established. The method has been implemented into a computer code for two‐dimensional geometries, whose results are presented here. A comparison with the analytical results already shows excellent agreement for coarse discretizations.