The interregional differences in the standard of living and well-being of the population are quite large. In this regard, a relevant question is the trend of this situation: Is interregional inequality increasing or decreasing? Interregional inequality could be reflected in different characteristics of the economy and one of them is income inequality. In this study, I concentrate on the Russian Federation – a large country with various regions. The purposes of the study are, first, to determine the trend in the dynamics of interregional income inequality, and second, to determine whether there is a convergence of average income per capita in the regions of Russia. By a preliminary basic hypothesis, I expect a tendency to multimodal income distribution at least to such an extent that 2 big income classes exist, such as “poor” and “rich” regions. The main method of the analysis is the distribution dynamics approach with the construction of a transitive probability matrix and the calculation of an ergodic distribution. The indicator under study is the real income per capita, obtained from the nominal income per capita, adjusted for the level of regional prices by taking into account the cost of a fixed set of goods and services. The spatial and temporal boundaries are defined as 79 regions of the Russian Federation, in the period from 2002 to 2019. As a result of our study, according to the ergodic distribution obtained (long-term forecast), there is a tendency toward convergence, but with a polarization in particular. There are also other tendencies: the percentage of areas with income at or above the average Russian income will increase, while the portion of the poorest areas will decrease. The results of this study are important for both the population and the government, because the results may provide some guidance as to whether some policies can possibly change the cross-region income distribution the country is heading towards.