Accurate flux approximations are of interest in many applications and this is particularly true for fluid-structure interaction problems. Considering the corresponding spectral problem, the Least-Squares method involves the flux and the stress as independent variables approximated in a suitable $H$ (div)-conforming finite element spaces. This talk will discuss the applicability of the Least-Squares method for the determination of the corresponding elastoacoustic vibrations, and show that the resulting scheme provides a correct spectral approximation. Quasi-optimal error estimates and numerical experiments to confirm those will be provided.