In modern computational problems in mechanics and resistance of motherales, numerical methods are often used that use computers to perform volumetric calculations. One of the most widely used methods for analyzing structural strength is the finite element method (FEM). This method serves as a universal tool for solving a wide range of problems in the fields of continuum mechanics, heat exchange, hydrodynamic and electrodynamic calculations. One of the disadvantages of numerical methods compared to analytic methods is the large error of calculations when solving problems to compare with their exact solution. The present work examines the accuracy of the numerical solution of the problem of a beam held in equilibrium using only one rigid backstop with a given load obtained by the finite element method. The article analyzed the accuracy of the solution using two methods: the numerical method of finite elements and the analytical method of double integration.