Rotating machines in motion tend to exhibit undesired vibrations and are subject to critical operating situations. In many applications of components or equipment, such as turbines, compressors, electric motors and pumps, a considerable mass motor is mounted on a lightweight and flexible shaft supported on bearings. The imbalance in the rotors, added to effects such as axle damping, gyroscopic effect and fluid friction in the bearings, causes a certain bend in the shaft (spinning effect), compromising the rotor structure. It was proposed to analyze the dynamics of a Jeffcott rotor, a rotor model consisting of a flexible massless shaft supported between two bearings with a hard disk mounted in the center of the shaft. The high cost of the experimental tests leads to consider a numerical simulation to verify the design of rotating equipment without the need to perform different experiments for each type of variable to be studied. In this way, the analytical response of this type of rotor was evaluated and the results were compared with those of a numerical simulation model using RecurDyn® software. It was also evaluated the influence of the rigidity and damping properties of a bearing in the attenuation of the vibrations of rotating axes.