Fracture of initially crack-free bodies often occurs due to plastic instabilities known as shear bands. Previous computer simulations advanced a myriad of mechanisms to rationalize shear banding. However, they were restricted to planar geometries. We investigate the relevance of anisotropic plasticity by picking an axisymmetric tensile test rig, in which shear localization is rarely observed. The three-dimensional finite-element simulations of shear banding in this type of specimens are the first of their kind. The micromechanical modeling covers a range of competing mechanisms believed to be responsible for such failure. We show that anisotropic plasticity can effectively trigger shear bands thereby causing failure of ductile solids. Our results enable shear fracture to be rationalized in ductile rocks and mitigated against in designing advanced materials.