Abstract: The comparison between the eigenfrequencies of an elastic target and the resonance characteristics of scattering and radiation from the elastic target is studied. By applying the minimum potential principle, the finite element equation for the elastic object is established, and by linking the integration formulation of the object surface, the eigen equation of the elastic target in water is obtained. The Lanczos algorithm is used to calculate the eigenvalue, and the inherent vibration modes are analyzed. The comparison between the eigenfrequencies and the acoustic characteristics validates that the strong resonant scattering and radiation are produced at the eigenfrequnecies, and the amplitudes of acoustic scattering and radiation depend on the power excitation mode. The analysis of the inherent vibration modes of a complex slender shell with an attached structure show that the lower vibration modes assume the axial and radial vibrations of the main body; the attached structure has no effect on the vibrations, but it makes the eigenfrequencies of the first several orders move to higher frequencies. As the frequency increases, the inherent vibration modes assume the vibrations of main body and attached structure, but the axial vibration is the dominant characteristic.