This paper mainly discussed over the years , many researchers in the definition of structure of the damage index under the earthquake , What is the damage index ? Means the structures in the role by the earthquake generated a series of reaction parameters , and followed by the calculation created out of a given process will quantify the degree of injury . Therefore , we can use damage index to understand the structure of the initial damage , and to determine the structure should be repaired or removed . When under the strong earthquake , structure began to change the natural frequency , and to judge the damage of structure by the frequency change . In the thesis , we use Least-square method as a method of structural system identification , to obtain the structure of the system damping ratio and frequency , then use the Newmark-β Method to verify the accuracy , and determine the damage of structure by Maximum softening and Damage Index of Stiffness . Finally , consider the material parameters and the displacement of the structures under cyclic loading and the energy dissipation of a combination of index . It is Park and Ang damage index to calculate the damage of column . Then use three indices mentioned above to make an order, and compare their advantages and disadvantages . Finally , we use the 1/2.25 scale of two –floor and two-span reinforced concrete structures of shaking table test by NCREE , to get the reaction and the structure of the material parameters as the examples to analyze . Then , through the results by system identification and damage indices to make a comparison and conclusion .