Corrugated web plates have been used in recent years as the webs of steel girders in bridge constructions thanks for their advantages, especially their superior shear capacities relative to stiffened flat webs. Therefore, they have been extensively investigated under shear compared with their limited investigations on the bending behaviour which was exclusively concentrated on the girders formed from the conventional normal strength steels. On the other hand, the use of high-strength steels (HSSs) in bridges has been increased when large and column-free spaces are key design issues. This paper focuses on the lateral-torsional buckling (LTB) of bridge girders with corrugated webs (BGCWs) built up from HSSs. This is done by using the commercially available finite element (FE) analysis package ABAQUS which has been used to generate parametric studies addressing the different affecting parameters on the behaviour of these girders. Simply-supported girders subjected to uniform bending, representing the worst case in LTB which is used in developing the member capacity design rules in different standards, are used in developing the current nonlinear FE models. The recently suggested warping constants in literature are used to compare the critical buckling moments with the elastic FE predictions. Then, the design model included in the Eurocode 3 is compared with the nonlinear strengths of the girders. The comparisons show that it provides conservative outcomes; therefore a modified version of the design model is suggested by using another buckling curve.