In parallel with the experimental study described in the companion paper (Zhao et al., submitted for publication), a numerical modelling programme has been carried out to investigate further the structural behaviour of stainless steel cross-sections under combined loading. The numerical models, which were developed using the finite element (FE) package ABAQUS, were initially validated against the experiments, showing the capability of the FE models to replicate the key test results, the full experimental load–deformation histories and the observed local buckling failure modes. Upon validation of the FE models, parametric studies were conducted to generate additional structural performance data over a wide range of cross-section slenderness and combinations of loading. The experimental and numerical results were then compared with the design capacity predictions from the current European Standard EN 1993-1-4 (2006) and American Specification SEI/ASCE-8 (2002) for stainless steel structures. The comparisons revealed that the current design standards can significantly under-estimate the resistance of stainless steel cross-sections subjected to combined loading; this under-prediction of capacity can be primarily attributed to the lack of consideration of strain hardening of the material under load. The Continuous Strength Method (CSM) is a deformation-based design approach that accounts for strain hardening and has been shown to provide accurate predictions of cross-sectional resistance under compression and bending, acting in isolation. In the present paper, proposals are made to extend the scope of the CSM to the case of combined loading. Comparisons between the CSM design proposals and the test and FE results indicated a high level of accuracy and consistency in the predictions. The reliability of the proposals was confirmed by means of statistical analyses according to EN 1990 (2002).