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 modelling technique are based on auto regression and regression analysis of time series for demographic indicators, simulation modelling and confidence intervals for model values of demographic indicators with taking into account a priori information and constraints on the model parameters and modelling process. Based on confidence intervals three scenarios of Russia's demographic development were developed: Low, Medium and High. On the time period 2013-2033 being investigated the demographic model to be constructed allows for the scenario variants to calculate one-year age structures for men and women, one-year age fertility, mortality and net migration rates and all necessary for analysis integral demographic indicators. The results of the multivariate analysis of the demographic processes in Russia in 2013-2033-time period to be carried out are described.