Steel girders with corrugated web plates (BGCWs) have already been used in many bridges around the world because they own several advantages compared with traditional plate girders with flat webs. They have considerably high shear resistances and provide weight saving by reducing the web thickness and by eliminating the use of transversal stiffeners. However, these girders practically have been designed based on half-scale experimental tests. On the other hand, it has been recently recognised that high strength steels (HSSs) provide designers with the opportunity of creating more slender and weight efficient structures than would be possible if the normal strength steels (NSSs) have been used. To gain benefit from the advantages of both the BGCWs and the HSSs in one structure, this research work is carried out to investigate the BGCWs built with HSSs which have seldom been explored in literature despite being utilised in the Pennsylvania Demonstration Bridge with corrugated web, USA, which was opened for service in 2005. Finite element models, by using ABAQUS programme, have been used to accomplish this investigation. They are firstly verified by comparing their results with the existing test results in literature. Then, extensive nonlinear parametric studies are generated considering the corrugation dimensions used in the available constructed bridges. The strengths of the girders are compared with the available design models and the best model calculating the ultimate shear strength is highlighted. Additionally, from this investigation, an understanding for the real behaviour of the BGCWs built with HSSs is established.