This book is devoted to mechanical models, variational formulations and discretization for calculating linear vibrations in the frequency domain of complex structures with arbitrary shape, coupled or not with external and internal acoustic fluids at rest. Such coupled systems are encountered in the area of internal and external noise prediction, reduction and control problems. The excitations can arise from different mechanisms such as mechanical forces applied to the structure, internal acoustic sources, external acoustic sources and external incident acoustic plane waves. These excitations can be deterministic or random. We are interested not only in the low-frequency domain for which modal analysis is suitable, but also in the medium-frequency domain for which additional mechanical modeling and appropriate solving methods are necessary. The main objective of the book is to present appropriate theoretical formulations, constructed so as to be directly applicable for developing computer codes for the numerical simulation of complex systems.