The research presented here seeks to address the key parameters influential on out-of-plane (OOP) instability of rectangular walls, which was observed in the 2010 Chile and the 2011 New Zealand earthquakes in some well-confined modern walls. For this purpose, a finite element model, previously verified for its capability to reliably simulate different failure modes of this type of structural walls, was adopted. The parametric matrix included a series of specimens designed to be tested by the authors and other specimens already tested by other researchers. The effect of slenderness (unsupported height-to-thickness) ratio, reinforcement ratio, length and axial load on the OOP response of these specimens is scrutinized using the predicted response of the boundary region longitudinal reinforcement at the elevation corresponding to the maximum OOP displacement in each case. For a given slenderness and longitudinal reinforcement ratio, development of a critical average tensile strain over a certain height can lead to formation of OOP instability in walls. Therefore, the effect of these parameters on the strain history, strain gradient along the wall height, as well as the stress–strain response of the longitudinal bars throughout the cyclic loading are evaluated and the variation of the OOP response attributable to the effect of each parameter is discussed. This parametric study indicated that the initiation of OOP displacement in doubly reinforced walls after unloading from a peak displacement and during reloading in the opposite direction is in line with the significant reduction of compressive stiffness (yielding in compression) in the boundary region longitudinal bars along a specific height (at least 60% of the wall height). Based on the findings of this study, an experimental campaign was designed and four of the parametric models were experimentally tested under in-plane cyclic loading. In addition to the parameters noted above, the effects of shear strength, boundary conditions and eccentricity of material properties across the wall thickness on the OOP response of the benchmark parametric model are also briefly discussed. The experimental observations as well as the numerical versus experimental comparisons are presented in a companion paper.