The mechanics of structures with initial stresses is a traditional part of structural mechanics. It is closely related to the problem of stability (buckling) of structures and structural elements. Note that the theory of stability of beams arose earlier than the theory of elastic bodies with initial stresses. The basic concepts of elastic stability of structures go back to works by Euler (1759) (beams) and Bryan (1891, 1888) (plates). Later, Hill (1958), Marguerre (1938), Prager (1947), Timoshemko and Goodier (1951), Trefftz (1930), Washizu (1992), and other researchers demonstrated that the problem of deformation of solids with initial stresses is related to variational principles and nonlinear problems in elasticity.