Although critical bucking shear stress of plate girders loaded mainly in shear have been studied for so many years by multiple researchers, but the matter of choosing the right boundary conditions at the junction between the web plate and the flange & stiffener is still a problem of Engineering judgment and standards approach. all current codes of practice and standards adopt a conservative design criterion by taking the simply supported boundary conditions at this junction. However, in this study, we have proved Two theoretical methods were employed to investigate such situation that the boundary conditions along the junction between the webs and the flanges as built-in and the other boundary conditions along the position of the vertical stiffeners are assumed to be simply supported due to the relatively small stiffness of the stiffeners could be reached. The first method using the minimum potential energy concept to obtain a semi-exact equation from which the interaction equation can be deduced. The second method is performed by using a finite element technique (ANSYS software) to investigate the effects of the geometric parameters on the boundary conditions at the juncture