Due to the growing number of corrugated webs in structure members such as buildings and bridges, their behaviour and strength should be extensively investigated. Accordingly, this paper is an extension of the experimental study conducted by the authors in the trapezoidally corrugated web girders (CWGs) under pure bending moment (PBM). This paper focus on the flexural behaviour of CWGs ,for highway bridges, and their lateral torsional buckling (LTB) strength. Linear and Comprehensive nonlinear finite element (FE) analysis using ABAQUS programme are employed. Firstly, the FE model is validated using experimental data then parametric study is conducted. Real bridges dimensions are used with short web height and variable spans to allow LTB to tack place. Girder length, given by the number of corrugation waves, changes from 4 waves to 36 waves by step of 4 waves. Furthermore, corrugated web height varies from 500mm to 300mm as well web thickness changes from 9mm to 12mm. Moreover, flange thickness varies from 50mm to 30mm and its width changes from 300mm and 500mm. Additionally, the corrugation angle varies from 36.9º to 45º cause changing in the corrugation thickness from 150mm to 177mm. Based on the elastic FE results, a comparison is conducted between the available equations in literature calculating the critical LTB stress using different warping constants such as Moon et al., Lindner and Nguyen. Additionally, a proposed design model is found to provide more suitable design strength of CWGs. Besides the Structural analysis of key parameters studies will be investigated and the obtained results are discussed. It is found that, flexure strength of CWGs increases with increasing the flange dimensions. Moreover, though Increasing the web height has a positive effect on the strength of the CWGs, using short girders height is more effective than large height ,specially, in relative long span girders.