(From the author’s abstract.) We consider a problem in three-dimensional linearized elasticity posed over a domain consisting of a plate with thickness \(2\varepsilon\) inserted into a solid. We assume that the Lamé constants of the material constituting the plate vary as \(\varepsilon^{-3}\), the density varies as \(\varepsilon^{-1}\), and the Lamé constants and density of the material constituting the “three-dimensional“ supporting structure vary as \(\varepsilon^{-2-s}\) where \(s\in ] 0,1]\). We prove the convergence of the eigenvalues of the three-dimensional problem as \(\varepsilon\) approaches zero either to the eigenvalues of the support, or to the eigenvalues of the plate, which then transversally vibrates at the limit. By contrast with earlier works, these “limit” eigenvalue problems are independent. Moroever, we can prove that the eigenfunctions of the “three-dimensional” supporting structure vary as \(\varepsilon^{2+s/2}\), while the eigenfunctions of the plate vary as \(\varepsilon^2\) for the tangential components, and as \(\varepsilon\) for the normal component.