Catastrophic structural failures are very harmful to humans’ lives. Theses failures can be created by minor damages, such as cracks, which can be propagated due to external loading and lead to the loss of structural integrity and stability. It is, therefore, worthwhile to have a reliable non-destructive damage detection (NDD) technique capable of detecting early-age damages on structures. Once the damages are discovered, repair or replacement can be made before their enlargement. In this thesis, investigations of the power flow in the plates containing single open crack are firstly performed. It is shown that the pattern and magnitude of the power flow are significantly changed only at the crack location. This trend also happens in the cases of the double- and triple-cracked plates. An NDD technique for plate structures based on these local changes of the power flow due to damages is introduced. The technique can effectively reveal damage location and severity using three power flow data measured from the tested plate as inputs for the reverse step. The characteristics of the nonlinear power flow induced by single and multiple breathing fatigue cracks on the cracked cantilever beam, namely super-harmonic resonance, are studied. The degree of nonlinearity of the power flow is shown to be dependent on the crack location, crack severity and amount of crack on the beam. This degree is used in conjunction with the surface fitting to determine the approximate location and severity of a crack on the beam. An NDD technique that can detect multiple-cracked cantilever beams is also proposed. This technique employs the power flow damage indices (DIs) obtained from the time-domain power flow plot to pinpoint the crack locations. The application capabilities of above three NDD techniques are presented through several numerical case studies. Effects of noise on each technique are also discussed.