•A comprehensive experimental programme including 34 cross-section tests has been carried out.•A range of cross-section sizes and stainless steel material grades has been investigated.•Fundamental data on the structural performance of stainless steel cross-sections under combined loading have been established. Stainless steel has been gaining increasing use in a variety of engineering applications due to its unique combination of mechanical properties, durability and aesthetics. Significant progress in the development of structural design guidance has been made in recent years, underpinned by sound research. However, an area that has remained relatively unexplored is that of combined loading. Testing and analysis of stainless steel cross-sections under combined axial load and bending is therefore the subject of the present paper and the companion paper (Zhao et al., submitted for publication). The experimental programme covers both austenitic and duplex stainless steels, and five cross-section sizes including three square hollow sections (SHS) and two rectangular hollow sections (RHS). In total, five stub column tests, five four-point bending tests, 20 uniaxial bending plus compression tests and four biaxial bending plus compression tests were carried out to investigate the cross-sectional behaviour of stainless steel tubular sections under combined loading. The initial loading eccentricities for the combined loading tests were varied to provide a wide range of bending moment-to-axial load ratios. For each type of test, the test setup, experimental procedures, full experimental load–deformation histories and key test results are reported in detail. All the experimental results are then employed in the companion paper (Zhao et al., submitted for publication) for the validation of finite element (FE) models, by means of which a series of parametric results is generated, and for the assessment of the design provisions given in EN 1993-1-4 (2006) and SEI/ASCE-8 (2002). Improved design rules for stainless steel cross-sections under combined loading are also sought through extension of the deformation-based Continuous Strength Method (CSM).