Origami-based sheet metal (OSM) bending uses the origami concept to form three-dimensional (3D) structures from a two-dimensional (2D) sheet by performing a series of bending operations. The OSM bending relies on material discontinuity (MD) lines to perform the bending operation during which the MDs are subjected to tension and shear load. Even though OSM bending is a process that is simple, cost-effective, and easy to integrate into mass production, the understanding of the OSM bending mechanics is limiting its wide application. Particularly, the deformation behavior of MDs under tension and shear load remains unknown. Hence, this study investigates the response of MDs to these loads using the standard tensile and shear tests. From these tests, the critical values for two different ductile fracture criteria (DFC) models are determined, and the possibility of a failure occurring in OSM bending can be predicted using the DFC models and the critical values. Results show that the load-bearing capability of the MDs is related to change in the effective cross-sectional area of an MD. The tensile and shear tests can provide a technique to predict failure in OSM bending. The results also show that the self-contact that can occur under shear load influences the maximum shear force and the accuracy of failure prediction.