Summary: In this paper we discuss numerical algorithms for solving a system of nonlinear PDEs arising in the modelling of two-phase flows in porous media, as well as the proper object-oriented implementation of these algorithms. A global pressure model for isothermal two-phase immiscible flow in porous media is considered. The finite-volume method is used for the space discretization of the system of PDEs. Different time-stepping discretizations and linearization approaches are discussed. The main concepts of the PDE software tool MfsolverC++ are given. Numerical results for one realistic problem are presented.