Mechanical properties of materials tend to deteriorate over time and thus become responsible for cracks and malfunctions in mechanical components or civil structures. Nondestructive ultrasonic wave analysis has proven to be a successful investigation method for inspecting mechanical properties of materials. This review has highlighted the main results of research in the field of non-linear ultrasonic wave investigations for the inspection of fatigue damage, thermal damage and chemical damage. In all three cases, non-linear ultrasonic wave survey method was effective in detecting first-stage damage.