This paper presents the study between the two methods for the recognition and identification of various elements damaged cases in beams. Damage causes changes in the vibration characteristics, including the modal properties. This affects the stiffness, damping, and mass. FEQD- Flexibility Energy Quotient Difference method which basically utilizes the flexibility matrix difference of undamaged and damaged structures using first mode of vibration is employed in this research work. Different types of beams are evaluated to verify the efficacy of the method. For these beams, single and multiple elements are damaged by reducing the bending stiffness in the elements. The results specify that the recommended method is efficient in identifying single and multiple damaged elements in beams.