The structural damage detection of mechanical structures in the early stage is an important research subject. A commonly used method for this purpose is based on the analysis of the structural vibration signals. Theoretically, the existence and location of the damage can be detected from the variation of the vibration signals. To this end, a proper method for vibration signal process is indispensable. The signal process method should exhibit high resolution and sensitivity for the detection of minor localized damage in the early stage. The Hilbert-Huang Transform (HHT), which has been successfully applied to many different fields in the last ten years, may provide a promising method for this purpose. This thesis studies the properties of HHT and the feasibility of its application to structural damage detection. To simplify the problem, we consider an extremely simply system - a simply supported beam. The damage of the system is represented by a spring with negative stiffness. The vibration signals of the beam with and without the damage are processed by the HHT. The existence of the damage can be identified from the change of the HHT spectra.