The textbook continues the presentation of the course "The theory of plasticity" , The beginning of which is presented in the book [10] ,. where the basic laws and general equations of the mechanics of a solid deformable body are given , methods of solving boundary problems of the modern theory of plasticity and solving some of the simplest problems of elastic-plastic deformation of structural elements . This manual presents the problems of flat deformation and flat stress state, extreme principles and energy methods of solving problems of plasticity theory (with consideration of limiting states of structural elements) , laws and basic equations of cyclic plasticity (with consideration of the theory of adaptability). The manual is recommended for senior students of the specialties "Physics of Strength" and "Basics of Design of Physical Installations", graduate students and engineering and technical workers specializing in the field of strength and rigidity of structural elements . Prepared in the framework of the Program for the creation and development of MEPhI .