The development of composites with self-diagnostic capabilities is based on the analysis of a mathematical model of the structure. The method is illustrated for a vibrating cantilevered plate and analyzed considering damping. Damage is modeled as an elastic joint, : and the spectrum of natural frequencies is calculated for different positions and magnitudes of the elastic joint. Small sensors consisting of tungsten filaments coated with ZnO are embedded in the plate, and their output is modeled The solution of the inverse problem depends on the position and extent of damage which can be uniquely solved if the system is not overdamped with respect to the primary frequency Higher modes have a decreasing contribution to the signal output; when the primary mode is overdamped, only the secondary frequency can be detected reliably. The solution to the inverse problem is no longer unique; there are as many as three different solutions (damage position and extent of damage) all of which produce the same signal output.