Two series of simply supported bending tests on aluminium alloy square and rectangular hollow sections have been performed. The test program comprised 14 three-point bending tests and 15 four-point bending tests. The test specimens were fabricated by extrusion from grades 6061-T6 and 6063-T5 heat-treated aluminium alloys, with width-to-thickness ratios ranging from 2.8 to 20.5. Measured geometric and material properties, together with the full load–deflection histories from the test specimens, were reported. Observed failure modes included local buckling, material yielding and tensile fracture. Further experimental data were gathered from the literature. Finite element (FE) models were developed and validated against the test results, and then used to perform parametric studies, in which a total of 132 numerical results were generated. The experimental and numerical results were used to evaluate the bending resistance provisions of the American [1], Australian/New Zealand [2] and European [3] Specifications, as well as the continuous strength method (CSM). The moment capacities predicted by the three design specifications were found to be generally conservative, while the CSM provided more accurate and more consistent predictions due to the recognition and systematic exploitation of strain hardening.