Abstract: In view of the low income level of a substantial part of the population in Russia and Kazakhstan, pronounced differentiation by income and social stratification, it is appropriate to introduce progressive taxation for individuals as required by the laws of economic development, despite the existing political imperative that determines the economic course. The article provides mathematical justification of the quantitative values of progressive scale based on the authorial software product of the model of optimal income tax for individuals that allows to accurately calculate the progressive rates considering various factors. The object of this research is the system of taxation of individuals; while the subject is the methods of quantitative determination of the boundaries of taxation of individuals with different income, consequences for the budget and population. The research employs the methods of comparison, generalization, statistical and economic-mathematical methods were used. The development of software product of the model of progressive income tax requires a particular method of mathematical substantiation of quantitative values, precision and convenience of economic-mathematical calculations. The authors developed the software product for personal income taxation based on the methodological provisions proposed by O. V. Kalinina. Such product allows calculating progressive rates of personal income tax, taking into consideration various factors. The conclusion is made that the transition from a flat to a progressive scale characterizes the social nature of redistribution of tax burden among population. Moreover, it would increase revenues into the state budget.