The crack prediction has been investigated by many engineers but the ductile fracture still plays the minor role in comparison to the brittle fracture or fatigue. The ductile cracking might occur in the cold working process of forward extrusion. This manufacturing process is used, among others, for the production of engine alternator shafts. The V-shape of such internal defects gave them the name chevron cracks and their danger arises from their invisibility on the product surface. One way how to non-destructively inspect these defects in products is to use the X-ray. On the other hand, it increases price of the product. Therefore, it is convenient to conduct the numerical computations in order to prevent the defect occurrence at the process design stage and manage the costs at a reasonable level. The process of forward extrusion in six reductions was examined. It was experimentally observed that there was no internal cracking after the fifth reduction and there were several chevron cracks after the sixth one. Then, the phenomenological ductile fracture criteria were calibrated in order to discuss their predictive ability which concerns the shape and number of cracks and also a state in which the onset of cracking was observed.