The modern-day popularity of tilt-up construction, shear walls and concrete cores in multi-storey buildings means that the construction of concrete walls with various boundary conditions and higher slenderness ratios, along with the presence of openings, has become common. The design of such elements under eccentric axial loads, however, could be outside the restrictions of current major design codes such as the Eurocode 2 (EC2-2004), the American Concrete Institute Code (ACI318-2014) and the Australian Concrete Standard (AS3600-2018). There have been many experimental and numerical studies on the behaviour of both one-way action walls and two-way action walls supported on four sides, with and without openings in the range of high slenderness ratios (up to 50). Efforts have also been made to develop design models capable of predicting the axial load capacity of such walls. However, research into the behaviour of two-way action walls supported on three sides (TW3S walls) is still relatively unexplored and further studies in this area are needed. Recent research has demonstrated that a rigid-plastic approach could be used to describe the behaviour of TW3S walls with and without openings. Although predictions obtained using the rigid-plastic approach showed reasonably good agreement with experimental test data, the scope of the analysis approach is considered limited. In this study, a validated finite element method, using the ABAQUS program, was employed to improve the rigid-plastic model, covering a broader spectrum of designs for axially-loaded TW3S walls. The reliability of the modified model was confirmed through comparisons with the available test data.