Construction of multi-storey reinforced concrete (RC) wall buildings in areas of moderate to high seismicity has become a common practice in several Latin-American countries such as Colombia, Peru, Ecuador and Mexico. The large material cost has led to the common practice of designing walls with only one layer of reinforcement and very low thickness. The earthquakes in Chile (2010) and New Zealand (2011) have shown that such design approach can induce out-of-plane failure of the walls under seismic action. In order to study the influence of different parameters on the out-of-plane response of thin members, an experimental campaign on RC columns was recently carried out at École Polytechnique Fédérale de Lausanne. These columns, axially loaded in cyclic tension-compression, represent the boundary element regions of RC walls, which correspond to the parts of the wall mainly involved in the instability mechanism. This paper illustrates the application of a shell model with truss elements to simulate the response of the tested specimens. The accuracy of the numerical model is assessed by comparison against the experimental results. It is shown that good estimates of the critical tensile strain that leads to out-of-plane instability as well as the out-of-plane displacement in cycles prior to failure are obtained. The failure mode is adequately simulated and also local behaviour is consistently reproduced. Therefore, the application of similar models to assess the vulnerability of thin RC walls to out-of-plane instability appears to be a relatively simple and robust numerical tool for engineering practice.