High strength steels, considered in the context of the structural Eurocodes, as steels with a yield strength over 460 MPa, are gaining increasing attention from structural engineers and researchers owing to their potential to enable lighter and more economic structures. This paper focuses on the bending strength of hot-finished high strength steel (HSS) square and rectangular hollow sections; the results of detailed experimental and numerical studies are presented and structural design rules for HSS cross-sections are proposed. A total of 22 in-plane bending tests, in three-point bending and four-point bending configurations, on HSS sections in grades S460 and S690 were conducted. The experimental results were replicated by means of non-linear finite element modelling. Upon validation of the finite element models, parametric studies were performed to assess the structural response of HSS sections over a wider range of cross-section slenderness, cross-section aspect ratio and moment gradient. The experimental results combined with the obtained numerical results were used to assess the suitability of the current European (EN 1993-1-1 and EN 1993-1-12) cross-section classification limits for HSS structural components. The reliability of the proposed cross-section classification limits was verified by means of the EN 1990 — Annex D method.