The article is about a new model of the dependence of the state’s human resource index on a set of factors. The human resource index does not have a global assessment methodology, but it is very important for government management. One of the methods for the formal assessment of the characteristics of a large socio-economic system is the reasonable ranking of particular criteria. Purpose . The aim is a development of recommendations for increasing the indicators of human development index at the state level using only formal methods of mathematical modeling. Materials and methods . Particular criteria described the human development index are selected. Their ranking is determined, which ensures the greatest smoothness of the annual trend. A set of mathematical models is designed. They are estimated both by approximating the initial data and by the quality of post-forecast. The second-order regression-differential model is chosen as the working one, its advantages and disadvantages in compare with the linear multifactor model are shown. The influence of changes in controlled and uncontrolled factors on indicators of the human development index is studied. System management features are shown. Conclusion . Some recommendations are formulated based on short-term forecasts to improve the human development index.