Cold-formed stainless steel oval hollow sections (OHS) offer the combined aesthetic appeal of circular hollow sections and stainless steel, together with the structural efficiency associated with cross-sections of differing geometric properties about their two principal axes. To date, no structural design guidance exists for these cross-sections, principally due to their relatively recent introduction and a lack of fundamental structural test data. This paper examines the structural response of stainless steel OHS compression members and presents design recommendations. A series of laboratory tests was carried out to generate fundamental structural performance data. Tensile coupon tests were initially performed to establish the basic material stress–strain characteristics of the sections. These were followed by stub column tests to determine the average compressive response of the cross-sections and flexural buckling tests to obtain ultimate load carrying capacity data for use in the determination of a suitable buckling curve for stainless steel OHS. Measurements of the geometric properties of the test specimens including initial imperfections were carried out. The full load–displacement responses of the specimens were recorded and have been presented herein. A finite element (FE) modelling programme was performed in parallel with the experimental study. Once the FE models had been validated against the test results, parametric studies were carried out to further investigate the influence of individual key parameters, including the aspect ratio and local slenderness of the cross-sections as well as the member slenderness. Based on the obtained experimental and numerical results, a class 3 limit for stainless steel OHS in compression and a suitable buckling curve for OHS columns have been proposed.