The structural behaviour and design of hot-rolled steel square and rectangular hollow sections (SHS and RHS) under combined axial compression and bending are studied in the present paper. Finite element (FE) models were developed and validated against existing experimental results on hot-rolled normal strength and high strength steel SHS and RHS under combined loading. Upon validation against the test results, an extensive parametric study was then performed with the aim of expanding the available structural performance data over a wide range of cross-section geometries, cross-section slendernesses, steel grades and loading scenarios. Both the experimentally and numerically obtained data were utilised for an assessment of the accuracy of the current design rules in European and American standards for hot-rolled steel tubular sections under combined loading. The comparisons revealed that the codified capacity predictions are generally somewhat conservative and scattered, due mainly to the neglect of strain hardening in the case of stocky cross-sections and the rather crude treatment of the partial spread of plasticity for Class 3 (semi-compact) cross-sections. The deformation-based continuous strength method (CSM) has been successfully applied to the design of hot-rolled steel cross-sections under isolated loading conditions (i.e. compression or bending), and shown to provide more accurate and consistent ultimate resistance predictions than the existing design provisions. This paper presents the first study to extend the CSM to the design of hot-rolled steel SHS and RHS, made of both normal and high strength steels, under combined loading, underpinned by both experimentally and numerically derived data points. Advantages of the proposed approach include eliminating the discontinuity in the current codified methods, yielding more accurate and consistent resistance predictions and providing knowledge of the level of strain required to reach a given resistance. The reliability of the proposed method is statistically verified in accordance with EN 1990.