Crack identification has special importance in the driving shaft performance to avoid rotor fracture. In this thesis, the dynamic of rotors such as rotary motion, mode shapes, natural frequencies, orbit and resonance is considered. A continuous model is presented for vibration analysis. Parameter identification of a static (non-rotating) rotor with an open crack, is based on two assumptions the cracked rotor is an Euler-Bernoulli beam with circular cross-section and the cracked region is modeled as a local flexibility with linear fracture mechanic. Through numerical analysis, the effects of the location and depth of the crack on the changes in the eigenfrequencies and mode shapes of the cracked rotor are investigated, and also the ratios of the changes in the first three eigenfrequencies are discussed for rotor with surface cracks. The rotor is modeled using finite elements method, while the crack is simulated as a weightless rotational spring. Increasing angular velocity or adding a disk as well as crack on the shaft reduces natural frequencies. Graphs of displacements and rotation for the cracked shaft and shaft without crack are plotted in three modes. Displacement difference graphs have a peak and rotation difference graphs of elements have bounces which identify the crack position. The Campbell diagram is plotted for the two shafts with different length. It is observed that increasing shaft length and angular velocity, forward whirling and backward whirling are seen more but this case is not valid in low angular velocity. Lateral vibration equation of the shafts without crack and also lateral vibration of the cracked shaft with two different boundary conditions (joint-joint and free-free) are calculated. Vibrational equations are solved by using boundary conditions of shaft and compatibility conditions in the crack position. By using first three frequencies and wavelet transform, the way to find depth and position of crack are described. Finally the modal analysis test is done on seven cracked steel shafts. The shafts have equal size and their only difference is in depth and position of cracks. The cracks are made on shafts by wire cut machine. The depth of any crack is 3 or 5 mm and their width is 0.5 mm. Frequency response of the vibration system are decomposed into four signals by wavelet transform (Daubechies Wavelets) and the position and the depth of cracks are accurately identified by using the first three frequencies. The calculated quantities for the depth and position of cracks are compared with actual quantities and finite elements results that have good agreement. Key Word: Crack detection, Wavelet transform, Vibration, Frequency response.