In a box girder cross‐section with inclined web panel, transverse compression may be introduced into the bottom panel from both sides in addition to constant longitudinal compressive stresses. In EN 1993‐1‐5, the only analytical method for determining the resistance of panels to biaxial compression is the Reduced Stress Method (RSM). However, the current rules were mainly derived for longitudinal stresses. Due to missing rules, in practice the longitudinal stiffeners need being verified according to flexural member buckling considering the transverse updrift forces.Therefore, in order to assess the real behaviour, a large parametric study of stiffened panels with closed longitudinal stiffeners under transverse compressive stresses was carried out using a verified numerical model. LBA and GMNIA are performed for each case. To apply the RSM, all critical buckling stresses were determined considering the torsional stiffness of stiffeners. According to EN 1993‐1‐5, the support of the edges of the panels parallel to the load direction should be set free when determining the critical stress for column‐like behaviour. In the case of a longitudinally stiffened panel under transverse stresses, it is not clear whether the support of the plate and the stiffeners or only the plate should be released. In this paper, these interpretations are discussed and results are compared. Finally, a simplified procedure to determine the global reduction factor of plate buckling for transverse stresses in a single step is proposed.