On the basis of a variational principle, a mixed finite element approach is developed to describe the linear dynamics of coupled fluid-structure interactions. The variables of acceleration in the elastic solid and pressure in the fluid are adopted as the arguments of the variational principle. These are chosen since they directly relate to many practical fluid-structure interaction dynamic problems involving free surface disturbances, e.g. a dam-water system, a fuel cell in an aircraft, etc. Matrix equations describing the motions are presented and four methods of solution discussed, each simplifying and approximating the matrix equations for easier application to solve various types of engineering problems. This is demonstrated by analysing a selection of fluid-structure interaction problems of practical interest. The examples illustrate the general principle and application of the described functional approach without need to resort to more complex dynamic problems which can be analysed in a similar manner.