The identification of local damages in structural elements is considered. In the proposed formulation, the damages are represented as local changes in structural stiffness and they are defined by a set of parameters. The main effort of this work is directed to the use of global measures of energy to indicate the local changes of stiffness. An idea of use of additional design parameters in order to optimize the experiment and to enlarge the sensitivity of objective functional with respect to damage parameters is applied. In order to accomplish this goal, the distribution of energy within the structural domain is optimized. Two cases, namely the eigenproblem and the structure under the static external load, are discussed. Simple illustrative example of identification of damage is discussed, and numerical results are presented.