The article solves the scientific problem of the lack of adaptation of gravity models for optimization of food supply of the country's population. On the example of the grain supply situation in the federal districts of Russia, the article demonstrates the relevance of the problem of improving the interregional grain exchange. A matrix of the food potential of the interregional grain exchange was created. A gravity model of interregional interaction of the constituent entities of the Russian Federation in grain supply on the basis of production indicators has been developed. Unlike the calculation of food potential, this model takes into account the inexpediency of grain supply from one scarce region to another. The parameters of the author's gravity model of interregional interaction of the constituent entities of the Russian Federation on grain supplies based on indicators of production in self-sufficient regions and consumption in scarce regions are determined. Due to the significant grain reserves and their surplus from year to year, the author extends the gravity model by using the reserve indicator as a measure of economic mass, which has not been implemented in the scientific community until now. The article is of interest to students and academic staff of economic universities and faculties, researchers, government officials, as well as other persons interested in the problems of food security, the application of gravity models in economics.