In this thesis, a model of two-phase flow through a porous medium is introduced and the finite volume method for its solution is described. The first chapter describes the porous medium and introduces the basic properties of the fluid flow that passes through it. In the second chapter, the mass conservation equation on the macroscale is introduced, by which we can predict the transport of mass within the system. The third chapter describes Darcy’s law and some additional macroscopic properties of fluids and porous media. Using the mass conservation equation and Darcy’s law, the fourth chapter introduces a two-phase flow of an immiscible fluid. Also, the 1D Buckley-Leverett equation is derived in the same chapter. The fifth chapter deals with the description of possible numerical ways for solving the introduced model. More precisely, for the finite volume method some of its versions (TPFA, MPFA and Box method) are described. After selecting one of them, using the IMPES algorithm the model can be solved efficiently. The sixth chapter provides the results and a description of three numerical simulations from different two-phase immiscible models. Simulations were made in the program library DuMu\(^x\).