Recent developments in performance-based seismic design and assessment approaches have emphasised the importance of properly assessing and limiting the residual (permanent) deformations typically sustained by a structure after a seismic event, even when designed according to current code provisions. In this contribution, the performance-based design framework for residual deformations, previously developed by the authors for 2-D regular structures, is further extended to the behaviour of 3-D irregular (asymmetric in-plan) buildings. The seismic response of a set single storey systems, comprising of seismic resisting frames, and made of alternative materials (concrete or steel), is investigated under uni-directional earthquake loading excitations. Different layouts in plan, leading to either torsionally unrestrained or restrained systems, are considered. Sensitivity analyses are carried out in order to identify the influence of varying levels of torsional restraint on the residual deformations/displacements in the response of a 3-D irregular building, the irregularity being given by an imposed mass eccentricity.