<p>We consider an algorithm for finding solutions to boundary-value problems of the two-dimensional elasticity theory by using physics-informed neural networks. The suggested approach makes it possible to reduce the boundary-value problems of the mechanics of continuous media to the problems of optimization, whereas the application of physics-informed neural networks within the framework of the considered approach makes it possible to reduce the solution of a broad class of problems to the construction of an error function of the general form. For the case of the Neumann conditions with constant forces given on the contour of the rectangular area, we indicate the explicit form of a neural-network function and the solution in displacements as a whole. To verify the proposed methodology, we perform the numerical analysis of the stress-strain state for a one-dimensional dynamic problem of longitudinal vibrations of a rod. The analyzed methodology can be extended to the case of three-dimensional problems of the elasticity theory, including piecewise homogeneous and, in a more general case, inhomogeneous media.</p>