Although a numerous methods exist for detecting damage in a structure using measured modal parameters, many of them require a correlated finite element model, or at least, modal data of the structure for the intact state as the baseline. For beam-like structures, curvature techniques, e.g., mode shape curvature and flexibility curvature have been applied to localize damage. An approximate flexibility matrix can be derived using a small number of vibration modes whose columns are referred to as flexibility shapes. In this paper, a damage localization method based on changes in flexibility shapes as well as its curvature is developed. Differential Quadrature Method (DQM) has been implemented to obtain the curvatures of flexibility shapes. It was shown that the method works well using the damaged model alone. To reduce the potential error due to differentiation of experimental data, a moving curve fit method has been implemented on flexibility shapes. The capability of the proposed method is demonstrated through numerical and experimental case studies.