This paper is focused on stainless steel square and rectangular hollow section (SHS and RHS) slender members loaded by a combination of compressive force and the bending moment. The study presents tests on 20 members, including initial imperfection measurements and material coupon tests. The tests take into consideration uniaxial bending to the major axis. The data obtained from the experimental study were subsequently used for validating an FE numerical model. A comprehensive numerical parametric study was carried out on all three common structural stainless steel groups: austenitic, ferritic and duplex. The cross-section slenderness and the cross-section aspect ratio (h/b), the non-dimensional member slenderness, the material stress–strain diagram (yield strength, ultimate strength, degree of non-linearity) and the ratio between the compressive force and the bending moment were set as the main parameters. Results of the numerical parametric study were compared with some of the existing procedures for stainless steel beam–column design. The main focus is on the proposal developed by Zhao et al., which is the procedure expected to be used in the new EN 1993-1-4. Although the method published by Zhao et al. has shown good prediction ability, a new design approach was proposed and its suitability demonstrated by a reliability study. The method is believed to be more general, as it uses a single formula for all grades of stainless steel, and also covers the effect of the section Class on the interaction between axial force and bending moment. •20 tests of stainless steel SHS and RHS beam–columns were conducted.•Numerical model was created, validated and used for a numerical parametric study.•Based on the numerical data, existing design procedures were compared.•A new general stainless steel SHS/RHS beam–column design procedure was developed.