This paper focuses on a new mathematical model of plastic bending of waveguide
tubes with rectangular cross-section. The analysis of the known approaches and decisions is
carried out, their shortcomings are shown and a new model of a thin-walled waveguide on the
basis of the theory of plates and shells is offered. The solution is obtained by combining the
semi-inverse Saint-Venant method and Airy functions. The received solution allows to
generalize the available private solutions and have good agreement with known private
empirical dependences for a plastic bending of tubes with rectangular cross-section.