This paper presents a damage identification technique based on the frequency changes between healthy and damaged beam structure. An algorithm based on frequency shift coefficient (FSC) is proposed, and the sensitivity of eigenfrequencies is studied. The method is tested by introducing an artificial damage, which depends on local stiffness reduction using five frequencies. The modal analysis technique is employed for healthy and damaged 2D Euler-Bernoulli beam modeled with Finite Element by using mass and stiffness matrices in order to provide natural frequencies. The effect of uncertainty on natural frequencies (0.1%, 0.2% and 0.3%) in damaged case is considered, and samples are used to estimate the average damage position and severity. In the beginning, the damage is localized and quantified. Then, the sensitivity of eigenfrequencies is investigated based on added uncertainty. The conclusion of analyses indicates that the algorithm correctly localizes and accurately estimates the damage by requiring a short amount of computational time.