Ductile fracture occurs due to micro-void nucleation, growth and finally coalescence into micro-crack. The ductile fracture criteria developed based on the microscopic phenomena of void nucleation, growth and coalescence along with a simple criterion based on the concept of the hydrostatic stress component at a point in the deformation zone falling to zero and compressive elsewhere are used to predict the fracture initiation in drawing (i.e. central bursting). Even though the first two criteria are based on microscopic description, the material parameters required are available for a few steels only and their determination involves difficult metallurgical experimentation. The above criteria used along with the results of Eulerian Rigid-Plastic and Elasto-Plastic formulations are presented in this paper. Finite element formulations for obtaining the generalized strain distribution and for obtaining the damage distribution by using the critical damage criteria are also presented. The present study shows that predictions based on the simple criterion are in good agreement with the experimental as well as numerical results published earlier and are, in general, conservative. Further, comparison of the predictions of the three criteria shows that the hydrostatic stress criterion is highly conservative and hence safe for die design.