The book provides for the first time the results of a systematic study of the variational principles of the theory of elasticity and sheaths in accordance with the theory of transformation of the variational problems of Courant and Hilbert. Along with the systematization of known variational principles, the book contains new results and generalizations. A system of complete and private functionalities, including mixed. The properties of functionals are studied not only from the standpoint of stationaryness, but also extremeness. Extreme and minimax properties of a number of known and new functionalities have been identified. A variational form of static-geometric analogy in shell theory. has been established The results are generalized to ribbed, multilinked, multilayer and other structural-anisotropic shells and used to analyze and solve a number of complex problems.