Structural Health Monitoring is a developing field that aims to monitor the performance of the structure and evaluate its condition by implementing damage detection strategies. In the past decades, many vibration based damage detection techniques have been developed. These techniques relate change in dynamic characteristics to the occurrence of damage in a structure. This thesis presents a new damage detection approach based on discrete wavelet analysis. The proposed method is verified using response of numerical models of frame structures under six different earthquake excitations, namely Kobe (1995), Athens (1999), Imperial Valley (1979), and another three earthquakes which were scaled to match the Omani seismic code (Loma Prieta, 1989; Cape Mendocino, 1992; and Chuetsu-oki, 2007). The histories are scaled to cause slight damage in structure. Eleven two dimensional frames with one, two, four, and eight stories having one, two, and four bays are considered. The numerical models consider the nonlinear behavior of the structural members and the response data are calculated by the nonlinear direct integration time history analysis. The method shows promising results and is able to detect extremely small damage and its time of occurrence for all ground motion cases. In addition, it provides good information about the general location of the damage. The ability to detect damage is observed to be more sensitive to the natural period of the structures rather than the average period of earthquake. The influence of noise is also studied by introducing white noise to the numerically generated response data.