The Continuous Strength Method provides excellent resistance predictions of stocky cross-sections under different loading conditions as it accounts for enhanced material properties, although the method is currently limited to crosssectional resistance. The axial stress in short columns potentially exceeds the yield strength as members are stable enough to allow partial yielding of non-slender cross-sections and the flexural buckling resistance prediction of these short columns is therefore usually underestimated, since equations currently codified in standards do not account for strain hardening effects. This paper presents the extension of the Continuous Strength Method to stainless steel Rectangular and Square Hollow Section columns, allowing strain hardening effects to be incorporated in the resistance prediction of members subjected to compression. The proposed approach is equivalent to the traditional approach for columns codified in different standards based on the Ayrton-Perry formulation but considers a different generalized imperfection parameter that depends on the cross-sectional slenderness and considered material, so strain hardening effects are directly introduced in the formulation. Results show that the proposed Continuous Strength Method approach provides improved predictions of the resistance of Rectangular and Square Hollow Section columns for all stainless steel grades. The reliability of the proposed approach has been demonstrated through the corresponding statistical analyses. Given the purely analytic nature of the proposed approach, it can be used for several materials, such as stainless steel, carbon steel and aluminium, and cross-section types for which the Continuous Strength Method has been defined. Finally, the better estimation of the flexural buckling behaviour of columns will have a direct impact on the accuracy of beam-column checks.