The behaviour of so-called 'cellular members' against lateral torsional buckling is investigated. These beams comprise regularly spaced web openings, and are especially used for their high resistance-to-weight ratio, the possibility of integrating service pipes within their height, and for aesthetic reasons. Such profiles usually exhibit a complex behaviour and many potential failure modes, including interactional local/global instability modes. Regarding global instability, members are usually designed by means of approximate design rules, which often lead to an unduly conservative girder, with beams sometimes showing up to 150% resistance reserve. This research work aims at improving this situation, through development of adequate design formulas. Both experimental and extensive numerical parametric studies are undertaken; a series of three full-scale tests is first performed, with the intention of using them to validate the derived finite-element models. Because the numerical models show very good agreement with the tests, they are then further used to gather a large set of numerical reference results where many parameters are varied: relative slenderness, steel grades, cross-sectional dimensions, bending moment distributions and the relative size of the openings. Finally, a new set of dedicated design rules is derived, which is demonstrated to be accurate and economic while leading to safe estimates of resistance when compared to all reference results.