There are two approaches to solve systems of linear equations Ax = b where for the matrix \(A\in\mathbb{R}^{m\times n}\) and vector \(b\in\mathbb{R}\) we have to determine vector \(x\in\mathbb{R}^n\). The first are so-called direct method in which the matrix A is presented as a product of simpler matrices, usually triangular. It allows us to solve simpler linear systems, and to come to the exact solution, where the complexity, or the number of necessary operations is \(O(n^3)\) . The second approach includes iterative methods, in which the error \( ||x^{k}− x||\) is small enough after much less operations then \(O(n^3)\) . Such methods do not define the solution directly, but iteratively, gradually, and we use them for solving big sparse systems of linear equations, who have a lot of zeros. With method like that, we construct sequence \(x^{(k)}\), \(k\in\mathbb{N}\) to which \(x^{(k)}\rightarrow x\) for \(k\rightarrow \infty\) The basic iterative methods for solving linear equation systems are Jacobi’s method, and Gauss-Seidel’s method. Successive over - relaxation method, shorter SOR method, is actually an extension or improvement of Gauss-Seidel method in that the auxiliary new approximation \(x^{(k+1)}\) is calculated by Gauss-Seidel method, and all that with purpose for improving the convergence. The goal of the modification was not to extend the class matrix for the iterative method converges, but speed up the convergence, as it is shown in examples.