Due to the growing number of used corrugated webs in structural members such as buildings and bridges, their behaviour and strength should extensively be investigated. Accordingly, this paper is an extension to the experimental study recently conducted by the authors on trapezoidally corrugated web girders (CWGs) under pure bending moment (PBM). In particular, this paper focuses on the flexural strengths of CWGs, for highway bridges, under the effect of elastic and inelastic lateral–torsional buckling (LTB). Currently, ABAQUS programme is employed to generate linear and nonlinear finite element (FE) analyses. Firstly, verified FE models using the above mentioned experimental data are adopted to generate parametric studies using large corrugation dimensions (used in actual bridges). Girder length, defined by the number of the corrugation waves, changes from 4 to 36 waves with an increment of 4 waves. Furthermore, changes in the corrugated web height, web thickness, flange thicknesses, flange widths and corrugation angle have been considered. The elastic FE results are compared with available prediction equations in the literature, which calculate the critical LTB stress using different warping constants. The results show that the calculations using Nguyen et al's method (2010) is the best. With regard to the design strength, the comparisons exhibit that original predictions of Lindner equation (1990), EC3-1-1 (2004) and AISC (2010) are highly conservative. Hence, modified versions for Lindner equation (1990), EC3-1-1 (2004) and AISC (2010) are suggested to provide more suitable design strengths for CWGs.