Applying an equilibrium approach to bifurcation the buckling of elastoplastic plates is investigated. The conditions for the onset of buckling are established for simply supported plates under biaxial loading conditions. The theory is also applied to study the elastoplastic buckling phenomena of the Yoshida Buckling Test (YBT). It demonstrated that sheet dimensions used in the original YBT specimen design does not take full advantage of the maximum value of the induced compressive stress. The peak value of the induced compressive stress, which is - 14% of the tension stress, occurs at a width to length ratio of the sheet of b/a = 0.914. While the same theoretical dimension ratio of a standard YBT specimen at b/a = 0.4 results in an average induced compressive stress to be about -6% of the tension stress. The sensitivity of the buckling load predictions to mechanical properties of material is examined for all possible combinations of ratios of applied stress resultants. It demonstrates that buckling not only depends on material mechanical properties, specimen size or part geometry, but also on loading and boundary constraints. Generally, buckle resistance is directly proportional to the work hardening index, and material anisotropy, however the effect of plastic anisotropy is small compared to other factors. Additionally, the metal thickness has a negative impact on buckle performance for thinner gauge sheets as down-gauging effort continues in the industry. It transpires that steel may not necessarily have a higher buckle resistance than aluminum sheets, contrary to common beliefs, since the critical strain required to initiate buckling is about 2-3 times less for steel due to its high plastic flexural rigidity. The elastoplastic bifurcation theory developed here can be a useful tool in studying the complicated buckling phenomena in aluminum sheets since not all process/material parameters can be investigated experimentally. Furthermore, it provides an insight and guidelines for sheet metal engineers to better develop forming dies during the process design stage.