The calculated study of the flow regimes of two-phase oil and water mixture in straight microchannels simulating a pore or crack in the rock formation was carried out. It was shown as a result of the literature survey that all modern, industrially developed methods of the oil recovery from the oil reservoirs is considered as unsatisfactory in all oil-producing countries. The average value of the final oil recovery is varied from 25% to 45%, so, it is easy to count, that residual or unrecoverable oil reserves in the subsoil reach an average of 55-75% of their initial values. Also, it was found, that the use of micro and nanotechnologies in a broad sense is one of the possible and promising ways to solve these problems. A numerical method called «Volume of Fluid» (VOF) was used to simulate the two-phase flows of oil and displacing agents in the considered microchannels. It was proposed to use the dimensionless number, called Regime number, to describe the different flow regimes of oil/water mixture and transitions between these regimes. The plug flow, the slug flow, the parallel flow and the emulsion flow regimes were observed.