The present paper examines the effect of local damage in elastic frames composed by Euler beams. The direct problems of undamaged and damaged frames are studied using the Wittrick-Williams algorithm. The related inverse problems of identifying material parameters in the undamaged structure and damage parameters, i.e. location and intensity, in the damaged frame are studied using procedures based on the comparison of numerical and pseudo-experimental natural frequencies. It is shown that the material parameters can be reliably determined and, with reference to the damaged frame, important considerations on the number of frequencies required in order to evaluate damage parameters are outlined. The sensitivity of the proposed procedure to experimental errors is also studied.