The present work presents a numerical method for the solution of two-dimensional flows of incompressible and immicible fluids in the presence of na interface. The conservation equations are discretized by the finite volume method. The interface modeling is based on the VOF method, in which the relative amount of the fluids in each control volume is described by a variable, denominated here as saturation. Once the distribution of this quantity is known, it is possible to construct the interface, when needed. The main contribution of this work is related to the reconstruction of the interface. For that purpose, it is taken into account the interface angle of inclination inside the control volume. This allows a more precise interface advection that it is usually found with the algorithms based on the VOF method. The interface angle inside a cell is obtained based on its saturation ando n the saturationof two adjacentcells crossed by the interface. By the presents scheme, the interface curvature needed to calculate the capillary pressure can then be easily obtained. Axi-symmetric domains were also considered. For these cases, an special treatment near the axis was necessary. Finally, the algorithm allows the specification of the interface contact angle with a solid surface. Several test problems were examined, presenting good results, validating the method.