The onset of flange wrinkling in the Swift cup test is analyzed as a plastic bifurcation problem. The flange is modelled as an annular plate made of an orthotropic elastic-plastic material that is isotropic in the plane of the plate. The critical drawing stress and displacement obtained employing a deformation theory of plasticity and a flow theory of plasticity are compared. The effects of flange geometry and material properties on wrinkling are investigated. Employing a simple linear elastic spring model of the blankholder, the effect of blankholder stiffness on wrinkling is studied. The present results for the critical stress at the onset of wrinkling and for the number of wrinkles are compared with those obtained previously employing a beam model of the flange.