In order to assess the seismic risk of structures, several methods based on pushover analysis have been developed. These methods are very useful in the case of symmetric structures because they can be easily approximated by means of a 2D model. In the case of asym-metric structures several improvements to the pushover analysis procedure have been proposed for considering the effect of asymmetry on the global response. However, such methods, in some cases, can be more expensive, from computational point of view, than the nonlinear dynamic analysis. In this article, we propose to assess the effect of the directionali-ty of the earthquake by using non-linear dynamic analysis and considering uncertainties in the mechanical properties of the materials and in the seismic action. We use as a case study a group of reinforced concrete buildings located in Lorca, Spain, damaged by the earthquake of May 2011. The results show a good agreement between the observed and the calculated damage.