Within the framework of the model of plasticity bands, we consider an elastoplastic problem of fracture mechanics of the development of plasticity bands near the tips of a central crack in a disk. We assume that, in the plane stressed state, plastic strains in the vicinity of the crack tip are localized along three plasticity bands (L1,L2, andL3) one of which is located on the continuation of the crack and the other two make nonzero angles with the direction of the crack and that, under the conditions of plane deformation, plastic strains are localized along two plasticity bands (L1 andL2). The band (L3) is modeled by a line of discontinuity of normal and tangential displacements and the bands (L1 andL2) are modeled by lines of discontinuity of tangential displacements. The lengths and orientations of these lines are determined in the process of numerical solution of the problem by the method of singular integral equations. The values of the crack tip opening displacement are also determined.