The brief description of the demographic model and modeling technique elaborated and used by the authors for investigating the trends of demographic development in Russia are given. The demographic model and the modeling technique are based on the using auto regression and regression analysis of time series for demographic indicators, simulation modeling and confidence intervals for model values of demographic indicators with taking into account a priori information and constraints on the model parameters and modeling process. On the basis of confidence intervals there were generated three scenarios of Russia’s demographic development: Low, Medium and High. On the time period 2013–2033 the demographic model allows for the scenario variants to calculate one-year age structures for men and women, one-year age fertility, mortality and migration increase rates and all necessary for analysis integral demographic indicators. The results of the multivariate analysis of the demographic processes in Russia on time period 2013–2033 are described. In particular according to these results it was found that fertility and natural increase of the population will decrease generally because of the influence of demographic wave; the total population will increase generally due to the increase of migration; the population will grow old; the coefficient of demographic load on the population will grow at decreasing rate.