This paper deals with the problems of management and forecasting of public debt of the Russian Federation, taking into account the situation after the August (1998) financial crisis. Three scenario forecasts of further development of the debt situation in the coming years depending on the degree of stabilization of the political and economic situation in the country are given. Scenario forecasts are made using a simulation mathematical model of the dynamics of public debt, which implements a scenario approach to solving management and forecasting problems. With the help of the proposed mathematical model, a scenario is found, the implementation of which will allow in the foreseeable future to bring the debt situation in Russia into line with European standards.