Many types of punching process have been utilized for the production of automobile parts and other related components. In the normal punching process that uses a punch and a die, both shear and fracture surfaces usually exist on the cutting surface. It is important to estimate the ratio of the shear surface to the cutting surface to produce highly accurate parts. To realize a smooth cutting surface of products, we have to apply the most appropriate tools and punching conditions to the process, taking account of the costs. The cutting surface of punching processes has been analyzed to study the ratio of the shear surface to the fracture surface by the finite element method (FEM). The criteria for fracture initiation on cutting surfaces have been proposed by several researchers. It is too difficult to identify the fracture criteria on cutting surfaces by simple experiments such as tensile tests, because the punching process has many complicated steps. In the present study, the finite element method is applied to several punching processes to evaluate the criteria of the ductile fracture functions proposed by Oyane and Cockcroft and Latham. As a result, the shape of cutting surfaces is affected by the clearance between the punch and the die, blank holding conditions, and the ductile fracture criterion.