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• Advanced FE modeling of cold-formed stainless steel (CFSS) EHS under combined loads. • A parametric study on the CFSS EHS stub-column behavior under combined loading. • Codified design rules and existing CSM for CFSS CHS under combined loading assessed. • Modified CSM and new interaction design curves for CFSS EHS under combined loading. • Reliability analyses for both the current and proposed design methods are presented. This paper aims to investigate the cross-section response of cold-formed stainless steel (CFSS) elliptical hollow sections (EHS) under combined biaxial bending and axial compression. In the present study, an advanced finite element (FE) model was adopted to perform a comprehensive parametric study for CFSS EHS under combined biaxial bending and axial compression, with different stainless steel alloys, as well as a broad range of cross-section sizes, aspect ratios, loading eccentricities and angles. Numerical results obtained from the parametric study were compared with the design strengths calculated by the current design rules in European code EN 1993-1-4, American specification SEI/ASCE 8-02 and Australian/New Zealand standard AS/NZS 4673. In addition, the Continuous Strength Method (CSM) for CFSS circular hollow sections (CHS) under combined actions, was also evaluated for the design of CFSS EHS under combined actions. The comparisons revealed that the current design codes EN 1993-1-4, SEI/ASCE 8-02 and AS/NZS 4673 provided conservative and very scattered predictions for CFSS EHS under combined actions. The existing CSM can provide more accurate predictions than the current design codes (i.e., AS/NZS 4673, EN 1993-1-4 and SEI/ASCE 8-02), but a further improvement is needed. In the present study, a modified CSM is proposed for CFSS EHS under combined actions, which can achieve reliable and accurate design predictions. [ABSTRACT FROM AUTHOR]