This work is related to the damage detection in a structure including the location and severity of the damage. It is shown that for the fixedfixed bar, fixed free bar and the cantilever beam, th eir finite element or finite difference discrete models built on the basis of th eir geometric parameters can be reconstructed from one eigenpair, that is, from on eigenvalue and its respective eigenvector. This reconstruction permits the devel opment of inverse eigenvalue procedures for damage detection in structures. The numer ical algorithms and some numerical examples are also given.