In this chapter, we present approximate methods for solving problems in structural dynamics, including evaluation of the eigenvalue problem. It goes without saying that the most popular method for solving the general multi-degree of freedom representation of a structure is the Finite Element Method (FEM), and most commercial software available today have evolved from the early FEM developments dating the 1960s, see the books by Zienkiewicz [1] in general and by Bathe and Wilson [2] in particular. During the same time, the Boundary Element Method (BEM) made its appearance, see for instance the book by Brebbia [3], as an alternative analysis method to the FEM. However, the BEM failed to become a universal method and is currently used for specialized problems, as for instance those involving the elastic full-space and the halfspace, as would be the case for soil-structure-interaction phenomena for buildings founded on compliant soil and for buried pipelines and tunnels. Finally, Rayleigh’s method dates from the late nineteenth century [4] and is built on a series of approximations for the modal shapes, starting with essentially a static displacement curve of the structure and slowly improving it until a convergence criterion is satisfied. This method is satisfactory if the fist couple of eigenmodes of a structure are sufficient for the ensuing dynamic analysis.