The book studies non-dimensional elastoplastic problems, the complexity of which consists not only in the non-linearity of the equations of the theory of plasticity in plastic zones, but, first of all, in the fact that the shape and size of the plastic region are not known in advance and must be determined. Shear, torsion, plane deformation, plane stress state and some other issues are considered. Not only the most significant analytical solutions are given, but also a summary of some numerical results in this area. With a sufficiently high level of loads, local plastic zones arise near holes, grooves, corners, slots and the like structural or technological formations. Accounting for these zones is especially important for strength calculation, since the destruction of most structural elements is always preceded by local plastic deformation.