This paper cosiders the testing of the finite element method based on three-dimensional problems in the theory of elasticity using the curvilinear solid finite elements. These elements implemented in the scope of the thesis research [1, 5] and realized within Solver of the software package "LIRA-SAPR" with the number 39. The test based on comparison between the obtained results and precise analytical solution and another finite elements models which exist on the software. The theory of thin plates and shells created based on the correspondence creation, which follows the Kirchhoff-Love hypothesis. This theory does not allow taking into account the difference of the stress function over the thickness of the plate. The thickness increasing of such elements leads to an increase of inaccuracy when calculating the structures with stress concentrators. We can also get somewhat better results using the elements based on the Mindlin-Reissner plate theory, which takes into account the deformation of the transverse shear. It is possible to evaluate more correctly the stress-strain state of projected structures using curvilinear solid finite elements in the simulation and calculation of non-thin plates and shells. Convergence of the finite element method is an important characteristic, since it determines the suitability of a finite element for constructing simulations. Since the approximation, as a rule, gives an approximate description of the deformation distribution within an element, hence the results of the calculation of the construction generally are also approximate. That is why the question about the accuracy, stability and convergence of the solution obtained by the method of finite elements remains important. As a test, it is considered the following tasks. The Lame problem of the stress-strain situation of the thick-walled cylinder under the external and internal pressure. The bend of the hinged and fixed along the contour thick square plates under the action of a transverse uniformly distributed load. The results of the calculation are compared with the theoretical solutions contained in the works of Lurie A. [4], Donnell L. [2], Lisitsyn B. [3] and others. To compare the accuracy, the problems also was modeled using the isoparametric finite elements from SP "LIRA-SAPR" and the SP "SCAD Office". In the study of convergence of FEM while modeling the thick cylinder, it was defined the limits of applicability of the curvilinear finite element.