When solving dynamic problems, it is necessary to define in some way the damping of the structure. Generally, a damping term that depends on the velocities is incorporated directly into the dynamic equilibrium equation. To do this, we define a structural damping matrix, such as Rayleigh's, which is quite difficult to estimate. Once the damping has been defined, the problem is solved as a linear elastic one, what enters in contradiction with the fact that a dissipative phenomenon is being treated. In this chapter, an alternative with greater conceptual basis is described, which considers the structural damping based on a viscoelastic constitutive models in which the stress depends in some way on the strain velocity. In this way, the term of structural damping arises directly in the dynamic equilibrium equation, where the properties of the materials can be determined through simple laboratory tests.