In this paper, we study the cyclic bending of elastoplastic beams. The work presents an extension of the use of Pryzack's model, already successfully used for axial loading of a bar, to the bending of beams. Using this model, it is shown that an accurate analytical solution is obtained for stress, axial force and bending moment in the cross section for any given history of deformations and changes in curvature. In this case, we went from the main bodies (Hooke and Sen Venan) well known in the theory of plasticity. The paper shows how it is possible to design hysteresis loops M-k, for a given cyclic change in curvature, and obtain residual stresses, which are very important in engineering applications.