In the current paper, the radial, axial, rocking, and yawing vibrations of a rigid grinding spindle supported by a pair of angular contact ball bearings are studied. A computer program was developed to simulate the dynamic behaviour of the spindle and results are presented in the time, frequency, and waterfall diagrams. Results from the simulations for different spindle speeds show the characteristic ball passage frequency (BPF) (varying compliance) and its harmonics due to non-linear Hertzian contact between the balls and the races for even a defect free bearing. This behaviour is, of course, predicted theoretically, but most of the previous simulations only give the effect of BPF when it coincides with the natural frequencies of the system or under specific conditions. This paper will be a guide for researchers studying vibrations of a spindle supported by ball bearings as it describes the details of the theoretical background of the modelling and simulation.