Analytical methods for large-scale assessment of the seismic vulnerability of RC buildings have only recently become feasible due to a combination of advancements in the field of seismic hazard assessment and structural response analysis. In many of the original procedures to define analytical vulnerability curves, nonlinear time-history analyses of prototype structures with randomly varying structural characteristics were carried out for a set of representative earthquakes. However, running nonlinear dynamic analyses for a large number of structures is extremely time consuming and alternative methods have thus been sought. The method presented in this paper defines the nonlinear behaviour of a random population of buildings through a simplified pushover and displacement-based procedure. Displacement capacity limits are identified on the pushover curve and these limits are compared with the displacement demand from a response spectrum for each building in the random population, thus leading to the generation of vulnerability curves.