The algorithm of the heavy ball method, based on the principle of symmetry, to find a global extremum is described. The computer simulation of the method for the three test functions (Ackley, Griewank and Schwefel) is carried out. The results of the study of the efficiency of this algorithm are given. The results of mathematical modeling in the graphs, describing the process of convergence of representative points to the global optimum point of test functions, are shown. Conclusions about the efficacy of the described algorithm applied to optimization problems are drawn.