Abstract - In the framework of this study, we have obtained a mathematical model for maintaining the financial sustainability of PAYG pension systems. We introduce the term financial soundness, by which we understand the maintenance of a balance between the contributions to the pension system and the costs of pension payments. We have proved that the financial sustainability of PAYG systems depends on the growth rates of wages, the growth rate of contribution rates. And demographic factors such as the ratio of the number of pensioners and the working population. However, in the context of countries' competition for investment and the impossibility of increasing the rates of contributions to the pension system, as well as the limited business opportunities to increase wages, the financial sustainability of PAYG systems is determined only by demographic factors. Financial stability in such conditions is violated in case of excess of the rate of increase in pension payments over the rates of Support Ratio (ratio of working population and pensioners).