It is postulated that fracture occurs in an elastic-plastic, nonwork-hardening material subject to pure shear when a critical shear strain is attained throughout a critical volume of material. This postulate is combined with the classical equations of plasticity to predict when cracking will initiate from a notch at nominal shear stresses below the yield stress, when the crack will become unstable on increase of stress, and when unstable cracking will occur if a notch is cut while a constant nominal stress is maintained. Tests on aluminum foil under biaxial tensile stress show results similar to those predicted by the theory.