Usually, when determining the safety margins and reliability of structures and their
elements, it is sufficient to solve the boundary value problem of the theory of elasticity at small
deformations. With the development of innovative technologies and the widespread use of composite
materials, the calculation of materials at large deformations is required. The article formulates a twodimensional
boundary value problem of the theory of elasticity in finite deformations for a rectangular
region with different boundary conditions. The grid equations are compiled by the finite-difference
method. To solve nonlinear grid equations, an effective iterative method is proposed based on the
solution of finite-difference equations and boundary conditions with respect to the sought nodal
values, taking into account nonlinear terms. The distribution of displacements and stresses in a given
area is investigated and the numerical results are compared with the results obtained for boundary
value problems of the theory of elasticity at small deformations.