Cropping is a cutting process whereby opposing aligned blades create a shearing failure by exerting opposing forces normal to the surfaces of a metal sheet or plate. Building on recent efforts to quantify cropping, this paper formulates a plane strain elastic–plastic model of a plate subject to shearing action by opposing rigid platens. Shear failure at the local level is modeled by a cohesive zone characterized by the peak shear traction and the energy dissipated by shear failure process at the microscopic level. The model reveals the interplay between shear cracking and the extensive plastic shearing accompanying the cutting process. Specifically, it provides insight into the influence of the material’s microscopic shear strength and toughness on the total work of cropping. The computational model does not account for deformation of the cropping tool, friction between sliding surfaces, and material temperature and rate dependence.