The evaluation of  seismic vulnerability of existing buildings represents a subject of crucial importance whose result may greatly influence the decision on the use of the building itself. However, the actual codes allow the use of several procedures and structural models, that in many cases may produce dissimilar results and therefore lead to different conclusions about the actual seismic vulnerability of  the building. The problem regards all structural typologies and in particular reinforced concrete buildings and historical masonry buildings. In this work the seismic vulnerability of a nine-storey reinforced concrete building, not designed to resist to earthquake loading, is evaluated. Although the building has been designed for vertical loads only, its structure can withstand also horizontal forces due to the presence of reinforced concrete shear walls in the staircases. In order to investigate the collapse behavior of the building, if subjected to seismic loads, static and dynamic nonlinear analyses have been performed. Due to the irregular structural skeleton of the building the nonlinear static analyses have been conducted taking into account the contribution of several modes of vibrations. Besides a multi-modal push-over analysis with time invariant lateral force distributions, proposed by the authors,  also the modal push-over analysis, proposed by Chopra, has been performed. The results of the static nonlinear analyses have been compared, in the more vulnerable direction, with those obtained by an uncoupled response history analysis, also introduced by Chopra, and  by a full nonlinear time-history analysis.