Abstract: In order to solve the stiffness and mass identification problems of structural damage, two damage detection approaches based on measured responses are presented, i.e. the Multiple Frequency Excitation Identification (MFEI) method and the improved Single Frequency Excitation Identification (SFEI) method. In the MFEI method, the basic theory of structural damage is first introduced, and then the formulas to calculate stiffness damage index and the mass damage index are proposed, which is based on the measured response of multiple frequency excitations. In the improved SFEI method, the simplified localization method of structural damage is first presented according to the stiffness and mass characteristics, and then an improved iterative strategy is proposed to conduct the calculation. The simulation results demonstrate that: For trusses the MFEI method can identify the stiffness damage but hardly to identify the mass damage. However, the improved SFEI method can identify both the stiffness damage and the mass damage, and the accuracy of the improved SFEI method are higher than that of the MFEI method and the simplified SFEI method.