The present study reports a numerical investigation of water and CO2 (carbon dioxide) flooding at the pore scale of a porous medium. We use high resolution micro-computed tomography (micro-CT) images of Berea sandstone core to obtain the pore geometry. The numerical solution used for the simulation was carried out by a finite element based software package. Level Set method is used to determine the position of the interface between two immiscible fluids when oil is displaced by water and CO2, respectively. The present formulation is validated against single-phase flow through the porous structure. It is found that, fluid flow inside the pore space takes place through preferential inlet and outlet pores. For two-phase flow, it is observed that continuous displacement of oil occurs during water flooding but CO2 is able to displace oil at certain locations in the pores. Also, the separation of flow front is observed in the case of CO2 flooding. A quantitative comparison of the results obtained in two types of flooding simulations suggests that water displaces a higher volume of oil than CO2 in the time period for which the simulations are performed. (C) 2010 Elsevier Ltd. All rights reserved.