Modern methods of detection and identification of structural damage direct the activities of scientific groups towards the improvement of diagnostic methods using for example the phenomenon of mechanical wave propagation. Damage detection methods that use mechanical wave propagation in structural components are extremely effective. Many different numerical approaches are used to model this phenomenon, but, due to their universal nature, spectral methods are the most commonly used, of which there are several types. This paper reviews recent research efforts in the field to show basic differences and effectiveness of the two most common spectral methods used for modelling the wave propagation problem in terms of damage detection.