The livestock industry is increasingly taking its place in the economy of the Russian Federation. Its export potential is actively growing. Already, up to 10% of agricultural products are exported to foreign markets. The demand for food steadily increases during crises, which in turn increases the role of the veterinary service, whose tasks include protecting the country’s territory from the introduction of infectious diseases of animals from foreign countries; implementation of measures to prevent and eliminate infectious and other diseases in agricultural, domestic, zoo and other animals, fur-bearing animals, birds, fish and bees, as well as the implementation of plans of the regional veterinary service in the field of animal husbandry. The article assesses the validity of the possibilities and use of modern methods of analyzing and predicting the spread of animal morbidity, identifying cause-and-effect relationships and the extent of the spread of particularly dangerous animal diseases. The authors propose to consider the possibility of using the mathematical method of hierarchy analysis as a scientifically sound decisionmaking support tool when assessing the risk of introducing trans-border infectious animal diseases into previously prosperous territories of the Russian Federation. This approach can be used in the process of choosing the most appropriate alternative from several risk assessment options. The Hierarchy Analysis Method (MAI) is a mathematical tool for a qualitative systematic approach to solving decision-making problems. This method was developed by the American scientist Thomas Lewis Saati in 1970, since then it has been actively developing and widely used in practice. The hierarchy analysis method can be used not only to compare objects, but also to solve more complex management and forecasting tasks.