Bridges around the world have utilised individually the mono-symmetric I-section corrugated web girders and the high-strength steel materials (HSSs). However, based on open database, there has not been any investigation in the literature exploring the mono-symmetric corrugated web bridge girders (CWBGs) constructed from HSSs. The paper is, therefore, devoted to numerically explore the global buckling of such girders built up from S460, which has extensively been used in bridge construction globally. This has been made based on finite element models (FEMs) developed by ABAQUS programme. Note that this paper merely considers girders having unequal flanges, but are symmetrical with regard to their minor axis, and their wider flanges are always deemed under compression. The validity of the current FEMs has not only depended on the previous experience of the authors, but also on the comparison between the elastic critical buckling moments and the available prediction methods. Additionally, experimental test results of flat-webbed girders have been considered in the validation. Parametric study has been carried out on simply supported girders considering mainly the influences of the mono-symmetry ratio and corrugation dimensions on the flexural buckling performance of the CWBGs which utilise S460 HSS. Several conclusions have been found that might aid the structural engineers in designing efficient cross-sections in the future. Additionally, the ultimate loads of the current CWBGs have been compared with EC3 specifications, and two design failure modes have been found to take place in present parametric study; the tension flange yielding and the lateral-torsional buckling (LTB) of the compression flange. The results, generally, show that the recommended method by EC3, for equivalent welded sections, is the most suitable in predicting the strengths of the current girders. Though, two modifications have been suggested for EC3 strengths regarding the tension flange yielding design formula and the LTB curve of the girders with depth-to-width ratios ≤2.0. The modified EC3 strength is generally found to provide accurate predictions for the CWBGs which utilise S460 HSS.