This paper presents a computer modelling investigation of the dynamic behaviour of rotors supported by hydrodynamic bearings. The rotor is discretized into "nite elements. The #uid-"lm bearings are represented by non-linear forces that are linearized in the neighbourhood of the static equilibrium position. Particular emphasis is given to the modelling of impacts between rotor discs and their casings, for which two approaches are used, namely (i) Newton's impact theory and (ii) direct determination of contact forces using a contact sti!ness. In the "rst approach, the discs are assumed to be connected to the shaft by spring elements. The discs and the stationary part are considered to be absolutely rigid. Velocity components of the discs after the impact are calculated using the law of conservation of the momentum and moment of momentum. Dissipation of mechanical energy during impact is taken into account through the coe$cient of restitution. In the second approach local #exibility and damping in the contact area are assumed. Local deformation produces impact forces and moments acting on the shaft at the disc location. In both cases, Coulomb friction is assumed to act in the contact area. A modi"ed form of the Newmark method was applied to solve the resulting non-linear equations of motion. Both approaches make it possible to characterize the steady state forced vibration behaviour (periodic, quasi-periodic, chaotic). In addition, the second approach provides further information on the likely magnitude and time history of the impact forces, duration of impacts, etc. The two approaches are illustrated by examples involving imbalance excitation and kinematic excitation of the baseplate.