The theory of elasticity developed as a science due to the necessity of having theoretical methods for calculating the strength of parts of structures and machines. At present the theory of elasticity is a branch of mathematical physics that must be at the finger tips both of engineers and scientists studying the strength of structures and machines. The book Theory of Elasticity is a textbook for students of higher technical schools of the Soviet Union. It contains matter on the theory of stresses, the geometrical theory of strain, the torsion of prismatic bars and the bending of plates. It sets forth the theoretical fundamentals of the solution of elasticity problems in terms of displacement and stresses and shows the general methods of solving problems in the theory of elasticity. The book considers plane problems in Cartesian and in polar coordinates. In conclusion the author deals with the variational methods of elasticity.