Various formulations are reviewed in the case of linear vibration analysis of bounded fluid-structure systems for low modal density situations. Compressibility effects in the fluid for interior structural-acoustic problems, and free surface gravity effects, as well as for hydroelastic-sloshing interaction problems in the case of incompressible liquids, are examined. Those matrix models leading to symmetric matrix systems are then described using static well-posed behaviour of the irrotational fluid. In this respect, the fluid-structure boundary value problem, expressed in terms of fluid scalar field variables for the fluid (and displacement variables for the structure) is regularized for zero-frequency limit. Reduced order models are then investigated.