Thin reinforced concrete walls may fail due to out-of-plane instability when subjected to seismic loading. While previous numerical studies on wall instability have focused on the behaviour of members with two layers of vertical reinforcement, this work addresses the response of walls with a single layer of rebars. Such walls are particular prone to out-of-plane failure when subjected to cyclic in-plane loading. The numerical investigations herein performed simulate the aforementioned local behaviour and validate it against experimental measurements. A parametric study on the effect of boundary conditions shows that imposing an out-of-plane displacement or a rotation at the storey height increases the vulnerability to instability. It is also seen that the storey height itself is an influencing variable. The second part of this study proposes an improved equivalent boundary element model for the assessment of wall instability. Existing mechanical models, based on pinned-pinned boundary conditions, represent the boundary element over the height of the plastic hinge. This work shows that such models often underestimate the critical tensile strain triggering out-of-plane failure. A new equivalent boundary element model is proposed where a bilinear axial displacement profile defined a priori is applied. The latter is shown to satisfactorily approximate the vertical strain profile in wall boundary elements and to lead to better estimates of the critical strain triggering out-of-plane failure.