In the present paper, a Harmonic Balance Method (HBM) coupled with a pseudo-arc length continuation algorithm is presented for the prediction of the steady state behaviour of a rotor-stator contact problem. The ability of the HBM to reproduce the four most common phenomena encountered during rotor to stator contact situations (i.e. 'no-rub', 'full annular rub', 'partial rub' and 'backward whirl/whip') is investigated. A modified Jeffcott rotor model is used and results of the proposed algorithm are compared with traditional time marching solutions and analytical predictions. The advantages and limitations of the HBM for this kind of problem are analyzed. It is shown that the HBM is orders of magnitude faster than transient simulations, and provides very accurate results. However, in its current form it is unable to predict quasi-periodic behaviour. Detailed analysis of the transient solutions yields valuable information for the future extension of the HBM to efficient quasi-periodic simulations.