Before starting a numerical analysis of any structure or structure, it is necessary to create two complementary models: physical and mathematical. A mathematical model, in turn, converts a physical model into a system of mathematical equations that describe the behavior of an object under the influence of loads. For many structural calculation problems, mathematical model equations turn out to be linear algebraic equations. For example, when using the force method or the displacement method in the calculations of rod systems (trusses, frames, beams), the problem is reduced to solving a system of linear algebraic equations in which either the forces in the rods or the displacements in the nodes are unknown. Similar problems also arise in the framework of dynamic analysis of systems where the determination of natural frequencies and modes of oscillation is required. In addition, many problems in continuum mechanics related to the calculation of plates, shells and soil masses are described using partial differential equations. However, the analytical solution of these equations is achieved only in exceptional cases. For this reason, numerical methods are widely used for practical calculations, which lead to the formation of systems of linear or nonlinear algebraic equations. The choice of the type of numerical method used is determined by various criteria: versatility, accuracy of approximation, ease of implementation of the algorithm and requirements for computing resources are important aspects. In practice, methods must have reliability, minimizing errors, demonstrate good convergence, and be adaptable to different tasks. These methods include the finite difference method and the variation approach in conjunction with the grid problem solving technique. Moreover, each of the listed methods has many variations, depending on what purposes are used and in which branch of knowledge are used.