Given the widespread use of beam and plate in structures, it is essential to have a thorough understanding of girder behavior. According to buckling failure mode in plates, it is necessary to take measures in this regard. Delta stiffener is using this approach. Due to the lack of technical knowledge about these kinds of plate beam, it is necessary to find good geometric properties of the delta girder plates for both technically and economically optimization. Therefore, in this paper, by modeling and finite element analysis for simple girder (without Stiffener), beam hardening by longitudinal plate and beam using delta hardening behavior are examined under the effect of the bending moment. Finite element analysis of elastic buckling analysis is included. With the above analysis, the effect of longitudinal stiffener and Delta Girders in terms of economic considerations has been studied. Keywords: Elastic Buckling, Beam, Plate, Stiffener.