In this paper an improved bearing model is developed in order to investigate the vibrations of a ball bearing during run-up. The numerical bearing model was developed with the assumptions that the inner race has only 2 DOF and that the outer race is deformable in the radial direction, and is modelled with finite elements. The centrifugal load effect and the radial clearance are taken into account. The contact force for the balls is described by a nonlinear Hertzian contact deformation. Various surface defects due to local deformations are introduced into the developed model. The detailed geometry of the local defects is modelled as an impressed ellipsoid on the races and as a flattened sphere for the rolling balls. With the developed bearing model the transmission path of the bearing housing can be taken into account, since the outer ring can be coupled with the FE model of the housing. The obtained equations of motion were solved numerically with a modified Newmark time-integration method for the increasing rotational frequency of the shaft. The simulated vibrational response of the bearing with different local faults was used to test the suitability of the envelope analysis technique and the continuous wavelet transformation was used for the bearing-fault identification and classification.