Structural damage identification has recently become one of the most important topics for engineering structures due to its benefits in enhancing safety, reducing life-cycle cost, and providing guidance for system construction and maintenance. This research studies the accuracy of using displacement influence lines (DIL) and their derivatives (first and second derivative) for detecting structural damage characteristics (location and severity). The study includes analytical and numerical studies to investigate the sensitivity of displacement influence lines and their derivatives (first and second derivative) as a main parameter for damage identification. The results illustrate that the method can locate and quantify damage in both simply supported and continuous beams without the need for an optimization algorithm. Although, for simply supported beam, the optimal location of the displacement measurement point is at the middle of span. While, for continuous beam, one displacement sensor at the middle of each span enables locating the damages reliably. The advantages and disadvantages of using this index are also discussed.