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Accurate prediction of fractures that occur in a material during forming not only improves quality, but also reduces the amount of material that is discarded. Formability evaluation is generally performed using ductile fracture criteria or experimental forming limit diagrams (FLDs), but these require fracture tests to be conducted beforehand. The authors have established a formability evaluation method based on the three-dimensional local bifurcation theory, which is a highly general method that does not require fracture tests. A flow rule that takes into account the dependence on the direction of the stress rate is used in this method, which can track abrupt changes in the stress field, such as localized necking. In this study, the proposed method is applied to forming analyses such as square-cup drawing and hole-expansion tests to analytically verify the location and initiation timing of local bifurcation modes that may lead to failure.