In this paper, schemes for constructing solutions to boundary value problems for static calculation of flexible circular plates with the nonlinear theory of Lyava and Volmyr are presented. From the equations of the equilibrium system of the plates, given in curvilinear coordinates, the system of equilibrium equations for flexible round plates is obtained. Substituting the expressions for the efforts and shearing forces and introducing dimensionless quantities, we obtain a system of quasilinear quantities in displacements. To develop an automated system for static calculation of flexible round plates, we use central finite-difference schemes that approximate derivatives with second-order accuracy, we obtain a system of quasilinear algebraic equations. To test the constructed automatic system for static calculation, the difference equations are reduced to vector form. An implicit iterative process combined with the Gaussian elimination method is applied to the solution of the system of equations. When calculating iterative processes, it continues until the above conditions are met. After determining the required functions by the finite difference method, we calculate the calculated values. Using the obtained numerical results, we will construct their graphs.