The current codified treatment of local buckling in stainless steel cross-sections is based on the traditional cross-section classification framework and a simplified elastic, perfectly-plastic material model, providing consistency with the corresponding carbon steel design rules. However, the cross-section classification framework treats the cross-section as an assemblage of isolated plate elements without considering the beneficial element interaction effect, and the elastic, perfect-plastic material model neglects the pronounced strain hardening exhibited by stainless steels. These limitations have been generally found to result in unduly conservative and scattered resistance predictions through comparisons against previous test data. To address these shortcomings, a deformation-based continuous strength method (CSM) has been developed, which relates the strength of a cross-section to its deformation capacity and employs a bi-linear (elastic, linear hardening) material model to account for strain hardening. The CSM has been established for the design of doubly symmetric plated sections and circular hollow sections, and shown to yield a high level of design accuracy and consistency. In this paper, the scope of application of the CSM is extended to cover the design of non-doubly symmetric cross-sections in bending. Global member buckling is not investigated. The developed design methodology and comparisons with existing test data and numerical results generated herein are described. Finally, reliability analysis is performed, which demonstrates the suitability of the proposals for inclusion in structural design codes.