For coupled structures surrounded by heavy fluids, it is difficult to obtain dispersion curves from an eigenvalue analysis, because the external fluid term in the coupled equation includes transcendental functions for frequency and wavenumber. Thus, in this study, the acoustic mass of the external fluid was approximated as a function of frequency or wavenumber only. The coupled equation can then be used to calculate eigenvalues, and can estimate dispersion curves from an eigenvalue analysis. Because of this assumption, those dispersion curves will contain errors. Accordingly, those errors were evaluated in this study through a comparison with a dispersion curve derived from forced responses. The acoustic mass was also evaluated for a water-loaded plate; this can be formulated theoretically. As a result, the acoustic mass is less sensitive to frequency changes than wavenumber changes, and using the fluid term defined at a low frequency has advantages when estimating the dispersion curve. Finally, the generality of the proposed method was identified through the application for a submerged cylindrical shell.