This article discusses physical analysis, including slab method and upper-bound method and slip-line field analysis, for calculating stress states in plastic deformation processes. It presents various validation standards and models for evaluating the criterion of fracture for use in finite-element analyses of deformation processing. The article reviews the Cockcroft-Latham criterion of fracture and its reformulated extension for analysing the fracture locus for compression. It concludes with information on fundamental fracture models.