Wrinkling is one of major defects in sheet metal forming processes. Wrinkling initiation and growth is influenced by many factors such as mechanical properties of the sheet material, geometry of the sheet and contact conditions. The analysis of wrinkling in a plastically deforming body is rather difficult because the effects of the above-mentioned factors are rather complex and the instability behavior may show wide variations even for small deviations of the factors. In this work, the bifurcation theory is introduced for the finite element analysis of the instability behavior of a thin sheet with initially sound geometry and property. The instability limit is found by introducing a criterion scheme into the incremental analysis and the post-bifurcation behavior is analyzed by introducing the branching scheme. The initiation and growth of wrinkling in the elliptical cup deep drawing process are analyzed by the proposed algorithm. Through the finite element analysis of flange wrinkling in the elliptical cup deep drawing process, the mechanism of wrinkling initiation is investigated and the effect of the tool and blank shape on wrinkling behavior is investigated.