In this book experimental and numerical investigations were carried out to identify the presence of a crack in a cylindrical overhanging rotor shaft with a propeller attached to the free end of the rotor. The rotor shaft was supported on a test frame using two supports. The rotor shaft had a cantilevered portion carrying the propeller. The rotor shaft was supported using ball bearings that were attached to the two test frame supports. In the experimental study, cracks of different depths were created on the shaft at the position of the maximum bending moment. The shaft's vibration responses for lateral and torsional vibrations were measured using an accelerometer, and shear strain gages fixed at three different locations, respectively. The response parameters of the shaft were then obtained using the modal analysis software, LMS Test LabTM. These experimental results were used to validate the numerical results obtained from a finite element analysis (ANSYS) using the beam element, BEAM4, and the three-dimensional iso-parametric elements (element types 186 and 187).