The collection of problems of applied elasticity theory with solutions is intended to illustrate the theoretical course "Theory of elasticity", some of its addition and to help in its study. The textbook presents both classical problems of elasticity theory and standard methods of their solution, as well as problems that have various practical applications, and are characterized by characteristic methods of solution. All selected tasks have a specific nature of solving problems brought to the final formulas, the results of solutions are of interest for the practice of engineering calculations and can be applied in the development and implementation of mechanical structures. It is intended for senior students of the specialties "Physics of Strength" and "Basics of Design of Physical Installations" , and is also recommended for students of technical universities and institutes, the Theory of Elasticity and its Applications , Post-graduate students and technical engineers , specialized in the field of strength and rigidity of structural elements.