A simplified mathematical model has been developed based on Jeffcott rotor to investigate the dynamic behavior of cracked  shaft. Analysis has indicated the existance of unstable zones of operation at the vicinity of which rotor response is largely magnified. In general rotor response due to unbalance forces contain vibrations at 1/rev and 2/rev components while gravity excited vibration is characterized by 3/rev harmonics as well. The measured response curve of the rotor shows an increased shaft deflection at all speeds. Also a subcritical peak is detected. Comparing the analytical results with experimental measurements indicates that the mathematical model is very realistic.