This paper presents a model for the coupled torsional and lateral vibrations of unbalanced rotors that accounts for the rotor-to-stator rubbing. The system degrees of freedom, obtained using Lagrangian dynamics, are the rotor rigid-body rotation, the rotor torsional deformation and two orthogonal lateral de#ections of the rotor. The rubbing condition is modelled using the elastic impact-contact idealization, which consists of normal and tangential forces at the rotor-to-stator contact point. The model is solved using a predictive-corrective numerical integration algorithm. The system response orbits show clearly the rotor-to-stator impact contact in the start-up period. The inclusion of rotor torsional #exibility has introduced irregular rubbing orbits. Rotor response anisotropy is observed in the rubbing responses for both lateral and lateral-torsional models. Furthermore, a split in resonance is observed due to the rubbing condition when the rotor torsional #exibility is considered. Finally, numerical simulations for rotors with non-zero #uid-"lm bearing cross-coupling terms have mainly shown a reduction in the split in resonance due to rubbing e!ects.