The presence of cracks causes changes in the physical properties of a structure which introduces flexibility,and thus reducing the stiffness of the structure with an inherent reduction in modal natural frequencies. Consequently it leads to the change in the dynamic response of the beam. This paper focuses on the theoretical analysis of transverse vibration of a fixed beam and investigates the mode shape frequency. All the theoretical values are analyzed with the numerical method by using ANSYS software and co relate the theoretical values with the numerical values to find out percentage error between them.Also in this paper, a model for free vibration analysis of a beam with an open edge crack has been presented. Variations of natural frequencies due to crack at various locations and with varying crack depths have been studied. A parametric study has been carried out. The analysis was performed using ANSYS software. Most of the members of engineering structures operate under loading conditions, which may cause damages or cracks in overstressed zones. The presence of cracks in a structural member, such as a beam, causes local variations in stiffness, the magnitude of which mainly depends on the location and depth of the cracks. The presence of cracks causes changes in the physical properties of a structure which in turn alter its dynamic response characteristics. The monitoring of the changes in the response parameters of a structure has been widely used for the assessment of structural integrity, performance and safety. Irregular variations in the measured vibration response characteristics have been observed depending upon whether the crack is closed, open or breathing during vibration. The vibration behavior of cracked structures has been investigated by many researchers. The majority of published studies assume that the crack in a structural member always remains open during vibration. However, this assumption may not be valid when dynamic loadings are dominant. In such case, the crack breathes (opens and closes) regularly during vibration, inducing variations in the structural stiffness. These variations cause the structure to exhibit non-linear dynamic behavior. Christides and Barr (1) developed a one- dimensional cracked beam theory at same level of approximation as Bernoulli-Euler beam theory. Liang, Choy and Jialou Hu (3) presented an improved method of utilizing the weightless torsional spring model to determine the crack location and magnitude in a beam structure. Dimaragonas (4) presented a review on the topic of vibration of cracked structures. His review contains vibration of cracked rotors, bars, beams, plates, pipes, blades and shells. Shen and Chu (5) and Chati, Rand and Mukherjee (6) extended the cracked beam theory to account for opening and closing of the crack, the so called "breathing crack" model. Kisa and Brandon (7) used a bilinear stiffness model for taking into account the stiffness changes of a cracked beam in the crack location. They have introduced a contact stiffness matrix in their finite element model for the simulation of the effect of the crack closure which was added to the initial stiffness matrix at the crack location in a half period of the beam vibration. Saavedra and Cuitino (8) and Chondros, Dimarogonas and Yao (9) evaluated the additional flexibility that the crack generates in its vicinity using fracture mechanics theory. Zheng et al (10) the natural frequencies and mode shapes of a cracked beam are obtained using the finite element method. An overall additional flexibility matrix, instead of the local additional flexibility matrix, is added to the flexibility matrix of the corresponding intact beam element to obtain the total flexibility matrix, and therefore the stiffness matrix. Zsolt huszar (11) presented the quasi periodic opening and closings of cracks were analyzed for vibrating reinforced concrete beams by laboratory experiments and by numeric simulation. The linear analysis supplied lower and upper bounds for the natural frequencies. Owolabi, Swamidas and Seshadri (12) carried out experiments to detect the presence of crack in beams, and determine its location and size. Behzad, Ebrahimi and Meghdari (14) developed a continuous model for flexural vibration of beams with an edge crack perpendicular to the neutral plane. The model assumes that the displacement field is a superposition of the classical Euler- Bernoulli beam's displacement and of a displacement due to the crack. Shifrin (16) presented a new technique is proposed for calculating natural frequencies of a vibrating beam with an arbitrary finite number of transverse open cracks. Most of the researchers studied the effect of single crack on the dynamics of the structure. A local flexibility will reduce the stiffness of a structural member, thus reducing its natural frequency. Thus most popular parameter applied in identification methods is change in natural frequencies of structure caused by the