The influence of yield strength on the in-plane stability and design of structural steel square and rectangular hollow section (SHS and RHS) beam-columns under compression plus uniform bending is investigated in this study. Ten buckling tests were carried out on hot-finished S690 SHS 100×100×4 (in mm) specimens under combined compression plus uniaxial bending. Finite element (FE) models of SHS and RHS beam-columns were established, validated and employed to perform parametric studies, where supplementary buckling resistance data were numerically derived. Through comparisons with the test and FE data, shortcomings of the current EC3 beam-column interaction curves were revealed, particularly in the higher yield strength domain. A modified EC3 approach was developed accordingly, featuring more accurate compression end points and re-calibrated interaction factors, and was shown to significantly improve the design accuracy and consistency for both hot-finished and cold-formed SHS and RHS beam-columns over a wide spectrum of steel grades. Subsequent reliability analysis confirmed the applicability of the current EC3 partial safety factor to the proposed modified EC3 design approach.