Abstarct: Nowadays structures play a significant role in ensuring the security and welfare of the human community. If the structures are not properly designed, implemented and maintained, they may cause problems. Proper design and execution of a structure is of great importance in the performance of the structure. In the meantime, there are some structures that, in addition to proper design and implementation, should be monitored continuously for their health control, in order to avoid collapse in the structure and adverse consequences. Important structures that need to be monitored continuously include dams, bridges and historic structures. These structures will cause irreparable consequences due to their economic, political and social sensitivities if they fail. Structures in the course of their lifetime due to various factors such as applied loads, fatigue, corrosion, etc. are damaged. Structural damage detection is one of the most important areas in engineering societies. In recent years, aerospace engineers, mechanics and civil engineering have shown this interest and many researches have been carried out. In this thesis, structural damage detection for bending plates is investigated by the aid of topology optimization. The objective function for solving this optimization problem is the difference in the frequency response function (FRF) as well as the difference in the mode shapes of the damaged structure and the numerical model. It is also shown in this thesis that there is no need for intact structure data for damage detection purposes. So by using modal data obtained from damaged structures in two different times, location and intensity of the progressive damage can be detected. In this research, Finite element method is utilized for structural analysis. Damage in this problem is assumed as a reduction in the structural stiffness and impact of damage on structural mass has been neglected. Material distribution in this problem is modeled by solid isotropic material with penalization (SIMP) method. For this purpose, the density of each element is considered as the design variable of the optimization problem. The amount of density for each element is between 0 and 1. If the density of an element is between 1 and 0, it means corresponding element is damaged, and if density of an element is 1, it means that corresponding element is intact. In SIMP method a penalization coefficient is assigned. Applying this coefficient on densities results in converting them to nearly full or empty elements. On the other hand, this coefficient increases the sensitivity to damage. Therefore, in this thesis, continuation method has been used. In this method, the coefficient changes between two values (3 and 1 in this research). This coefficient decreases linearly during the optimization stages, so that at the beginning of the optimization steps, the large value (3) is chosen, so that the variables approach their true values faster. After reaching final iterations of optimization, due to the low difference between the values of the density of the numerical model and their actual values, the coefficient is equal to the smaller value (1) and coefficient remains constant until the end of the optimization process. MATLAB software is used for programming purposes in damage detection procedure. Mathematical methods have been used to solve the optimization problem. The efficiency and accuracy of the proposed method is illustrated using few numerical examples. According to the results obtained from the examples presented in this thesis, the accuracy of the proposed algorithm in identifying the location and intensity of damage is significant.