Based on two-dimensional plane stress and bifurcation functional from Hill's general theory in polar coordinate the critical condition for elastic wrinkling of the flange of a circular blank ( the wave number in the flange and wrinkled area) during the deep-drawing process are obtained analyticaly to improve the previous given results. In this analytical study, the elastic limitation of the material is also considered and to derive the bifurcation functional, the small and large deflection theoris are used and their results are compared to each other. The main advantage of the current research is obtainting an explicit solution and using the large deflection theory to detemine the critical conditions at onset of wrinkling.