Despite the development of nuclear and alternative energy, thermal power plants operating by burning fossil fuels (coal, petroleum products or natural gas) will retain a significant share in the energy balance for a long time. In this regard, it is of particular interest to reduce CO2 emissions from the combustion of organic fuels through its capture and subsequent use or burial. In our work, mathematical modeling of the two-stage process of membrane extraction of CO2 from the flue gases of a thermal power plant was carried out, taking into account the presence of water vapor and various operating modes of the membrane module. We used commercially available polymer membranes for gas separation in our simulations. The calculations showed: Taking into account the presence of water vapor makes it possible to reduce the required membrane area by 1.6 times; For the degree of CO2 extraction < 80% in one stage, cross-flow and counter-current modes provide equal indicators for the required membrane area, and the co-current mode turns out to be less advantageous already with a degree of CO2 extraction > 60%. In this regard, in the area of low CO2 extraction values at the first stage, any flow organization mode in the membrane module can be selected, and in the high area, a counter-current has a slight advantage over the cross-flow mode; An optimal combination of membrane areas in the first and second stages is shown to achieve the maximum CO2 concentration in the product stream; Polaris Gen-2 membranes provide the best performance after two-stage separation: the CO2 content in the product stream was > 85 mol% and > 90 mol% with a total recovery rate of 80 and 50%, respectively; PolyActive and PPO membranes provide equal indicators for the CO2 content in the product stream, but in the use of PolyActive, the required membrane area is 2.3 times less.