An accurate and consistent approach to the out-of-plane stability design of steel beams and structures utilising second-order inelastic analysis with strain limits is proposed. The method is implemented using computationally efficient beam elements, with the ultimate structural resistance defined either by (i) the ultimate load factor or (ii) the load factor at which a strain limit, determined on the basis of the continuous strength method (CSM), is attained, whichever occurs first. Thus far, the method has been established for the in-plane design of steel structures and structural components; in the present paper, its scope is extended, for the first time to the scenarios in which out-of-plane stability effects, with a focus on lateral–torsional buckling (LTB), govern. The accuracy and safety of the method are assessed against the results of nonlinear shell finite element (FE) modelling. It is shown that the proposed method consistently provides more accurate results than the traditional LTB design method of prEN 1993-1-1. In addition to its accuracy, the proposed approach also streamlines the design process by eliminating the need for cross-section classification and member design checks.