Rotor dynamics is the study of vibration behavior in axially symmetric rotating structures. Devices such as engines, motors, disk drives and turbines all develop characteristic inertia effects that can be analyzed to improve the design and decrease the possibility of failure. At higher rotational speeds, such as in a gas pumps, the inertia effects of the rotating parts must be consistently represented in order to accurately predict the rotor behavior. An important part of the inertia effects is the gyroscopic moment introduced by the precession motion of the vibrating rotor as it spins. As spin velocity increases, the gyroscopic moment acting on the rotor becomes critically significant. Not accounting for these effects at the design level can lead to bearing and/or support structure damage. The main objective of this project is to study the Rotor Dynamic behavior of the drive rotor shaft of the Dry screw vacuum pump. The design of the pump is considered from the one of the reputed pump manufacturing industry. The operational speed of the pump is 4500 rpm, whereas the maximum capable speed of the pump is 10,000 rpm. Rotating machinery produces vibrations depending on the unbalanced mass and gyroscopic effects. Thus an investigation is to be made on the rotor dynamic properties of the shaft to find the natural frequencies and critical speed. For this rotor dynamic analysis was carried out in ANSYS APDL and Workbench16 to find the natural frequencies and critical speeds in the range of 0 to 10000 rpm. Thus an effort is made to shift the mass moment of inertia of the shaft by varying the design of the shaft and to shift the critical frequency to the higher speeds of the shaft there by increasing the efficiency. The modal analysis is performed to find the natural frequencies and it is extended to harmonic analysis to plot the stresses and deflections at the critical speeds. The design of the rotor shaft is made in NX-CAD.