A method of solving the problem of synthesis of optimal vventilation systems for coal mines, relying on the method of economic-mathematical modeling, is considered. The main analytical dependences for the calculation of different items of costs and limitations imposed on the economic-mathematical model are presented. These relations and limitations make it possible to take into account a considerable number of influencing factors and to realize optimization of the ventilation systems of coal mines by the cost criterion taking into account the laws of networks and mining engineering requirements.