Experimental and numerical cup drawing process has been investigated on 0.65 mm zinc sheets. The cup exhibits anisotropic earrings due to the material microstructure. The material formability is studied through elliptical bulge tests in the rolling, diagonal and transverse direction. High anisotropy of the formability is observed. The numerical simulation of cup drawing is then made and demonstrates the correct fitting with experimental results. A stress formability criterion developed by Jansen et al. [14] is then implemented into a finite element method software and applied to predict the material rupture observed for some process conditions. The risk zone of the cup is subjected to some strain path changes according to the simulation whereas the strain value does not explain the rupture according to the experimental formability measured by the bulge tests. It has been shown that the rupture is due to some critical stresses, which are reached in the risk zone of the cup. The use of the stress criterion and its non-dependence on the strain path change allows the fracture prediction. Finally, the numerical fracture propagation by the "kill element method", as briefly discussed by Bouchard et al. [4], is used and shows a good similarity with the experience.