Rocking post-tensioned steel frames capitalise on the use of rocking joints, and unbonded post-tensioning strands to provide self-centring action. Investigations on the complex and unconventional nonlinear dy- namics of tied rocking steel frames, exclusive of supplemental damping methods, are presently limited. Increasing levels of energy-dissipation reduce the probability of observing nonlinear dynamic phenomena such as co-existing (high/low) amplitude responses at and around the system’s nonlinear resonance. To this end, a finite element (FE) modelling framework is presented, validated and extended to multi-storey steel buildings. It is shown that the simulation strategies proposed enable an accurate representation of the complex nonlinear dynamics of self-centring structures, over a wide range of excitation frequencies and amplitudes. The methodology, applied to multi-storey steel frames, captures the presence of sub-harmonic resonances and higher-modes. It is also demonstrated that the additional demands observed in the rocking columns are the consequence of the asymmetry of the member boundary conditions.