System identification is an emerging area in engineering fields. To assess the present health of important structures is necessary to know the status of the health of structure and subsequently to improve the health of the structure. In this work, using the finite element software, a simple structural member like beam is modeled. A simply supported beam is taken and crack is initiated at the bottom of the beam along it's width by reducing the cross section in different location. Free vibration analysis is performed using FEM software SAP2000. There is a difference between the frequencies of cracked and un-cracked beam. From this analysis it can be predicted that there is damage in the beam, but location of the damage cannot be detected. For this, mode shape to be found out. This concept can be used to know in the real life structure whether there is any damage or not using the non-destructive techniques.