The paper deals with numerical modelling of carbon dioxide capture by amine solvent from flue gases in post-combustion technology. A complex flow system including a countercurrent two-phase flow in a porous region, chemical reaction and heat transfer is considered to resolve CO2 absorption. In order to approach the hydrodynamics of the process a two-fluid Eulerian model was applied. At the present stage of model development only the first part of the cycle, i.e. CO2 absorption was included. A series of parametric simulations has shown that carbon dioxide capture efficiency is mostly influenced by the ratio of liquid (aqueous amine solution) to gas (flue gases) mass fluxes. Good consistency of numerical results with experimental data acquired at a small-scale laboratory CO2 capture installation (at the Institute for Chemical Processing of Coal, Zabrze, Poland) has proved the reliability of the model.