There is a general interest in civil engineering to quantify the damage produced in structures by catastrophic actions. It would be convenient, from a practical point of view, to describe the state of a structure by means of a single figure that clarifies whether the structure is capable of supporting the service charges or not; if it will survive to another extraordinary load in the future; how does the present damaged state influence in its future behavior; where the most damaged points are located; what capacity of resistance remains in each point; and, in general, all kind of information that help to make design or repair decisions. The authors have proposed a solution to this problem in the specific case of earthquakes acting upon reinforced concrete building structures. A methodology has been formulated for the definition of an index of damage that can be typified for all the structures belonging to the same class and that allows classifying them according to their seismic vulnerability. In the monograph, simple beam structures are first studied in order to better describe the concepts involved and the parameters that influence the solution to the problem. The developed methodology, which models the structures using the finite element method, is directly and easily extended to shells, plates or 3D solids. The fundamental idea of this work is to apply constitutive equations formulated in 3D at a material point instead of using constitutive laws formulated in generalized forces-displacements such as, for example, bending moment-curvature, shear force-angular distortion, etc. This allows modeling the behavior of composite materials directly since for each component material its own constitutive law is considered. In this way, it is sufficient to have a single 3D constitutive model and a methodology to calculate the components of the stress and strain tensors at any point of the beam section.