The Continuous Strength Method (CSM) is a deformation based design approach that provides accurate cross-section resistance predictions by making rational allowance for the interaction between cross-section elements, the partial spread of plasticity and the beneficial effects of strain hardening. The CSM can be used in conjunction with advanced analysis for the design of members and frames, but, for hand calculations, member-level stability checks are currently limited to stainless steel hollow section columns failing by flexural buckling. Extension to the design of stainless steel members subjected to combined compression and bending moment is presented in this paper. The analysis is based on numerical results and existing experimental data collected from the literature on stainless steel hollow section members, including members with stocky and slender cross-sections. Comparisons demonstrate that the adoption of the CSM design equations in conjunction with both current and revised interaction factors considerably improves the accuracy of beam-column capacity predictions for members with stocky cross-sections. The analysis on beam-columns with slender sections shows that similar resistance predictions are obtained using Eurocode 3 and the CSM. The reliability of the proposed approach is demonstrated through statistical analyses performed in accordance with EN1990.