In this paper, the radial and axial vibrations of a rigid shaft supported by a pair of angular contact ball bearings are studied. The effect on the shaft vibration of varying the preload and the number of balls in the bearings is investigated when the bearings are perfect. For perfect bearings the vibrations occur at the ball passage frequency. The amplitudes of these vibrations are shown to be considerably reduced if the preload and number of balls are correctly selected. All results show that the vibration characteristics of the shaft and its bearings change when the bearings operate in different regions of their nonlinear load-deflection characteristics. This implies that the preload and the number of balls in a ball bearing are two of the important governing parameters affecting its dynamic behavior and have to be considered at the design stage.