A parabolic arch has been studied in its undamaged and damaged states. The damage consists in a notch that reduces the height of the cross section at a given abscissa. A damage identification technique, based on the minimization of an objective function which measures the differences between numerical and experimental variations of natural frequencies between the undamaged and damaged states, is presented. First, pseudo-experimental data were used to study the ill-conditioning of the inverse problem and to investigate the uniqueness of the solution. Different damage configurations were considered to assess the reliability of the identification procedure. Then, the identification procedure was applied to an experimental case, where frequencies were obtained by impulsive tests on the arch.