Based on two-dimensional plane stress wrinkling model of an elastic annular plate and a bifurcation functional from Hill s general theory of uniqueness for polar coordinate, the critical conditions for the elastic wrinkling of the flange of a circular blank during the deep-drawing process are obtained analyticaly to improve upon previously given results. In addition to critical conditions for onset of elastic wrinkling of the flange, the elastic limitation of the material is also be considered. To obtained explicit conditions for onset of elastic wrinkling small and large deflection theoris is used. The main advantage of this research is using large deflection theory and also obtaining an analytical and explicit solutions for critical conditions on onset of wrinkling

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