The paper shows the importance of managing migration processes for stabilizing the labor market in order to determine the country (region) population categories and labor resources, as well as develop economic measures to stimulate the migration inflow (outflow) of the population in the necessary scales and directions to increase the contribution of external migrations to the demographic and labor potential of the country, and changes in the direction of internal migration flows in accordance with socio-economic and national interests mi country and its regions. Mathematical and economic-mathematical modeling in the management of labor migration is considered as an integral part of the mechanism for stabilizing the region’s labor market.