The present work evaluates the possibility of using dynamic data to assess structural integrity. It addresses the problem of understanding when it is sufficient to measure and use only natural frequencies, thus avoiding the need to measure modal shapes. The classic problem of detecting damage in beams, or beam assemblies, due to concentrated cracks, or damage spread over a structural member is dealt with. Damage is represented as a decrease in stiffness and linear behaviour before and after the event assumed to have caused damage is considered. Damage is restricted to a few unknown sections or elements, so that only the modification of few parameters of the system need to be determined. This study thus rejects assumptions unrelated to the physical aspects of the problem, in contrast to many papers on the subject. The amount of data to locate and quantify damage correctly is discussed; general considerations lead to the conclusion that a unique and reliable estimate of the damage can be obtained using only few additional frequency data with respect to the number of damaged zones. Continuous and discrete (finite element) models are examined. Finally the paper considers the applications to both analytical and experimental data of the procedure developed, which takes account of the peculiar characteristics of damage detection problem.