The problem of two-phase flow of incompressible fluids through anisotropic porous media in the gravity field is considered. Similarity criteria characterizing the flow directions of the displacing and displaced fluids are determined. The regimes of displacement from an anisotropic formation are classified within the framework of study of numerical solutions to the profile problem of flow through an anisotropic porous medium. It is shown that there are four regimes corresponding to qualitatively different flows. Their effectiveness is compared in terms of the coefficient of fluid extraction from the formation and the displacement sweep factor. The influence of the capillary pressure on the displacement efficiency in various flow regimes is studied. It is shown that in some cases increase in the influence of the capillary pressure leads to increase in the displacement coefficient, while in other regimes, on the contrary, to its decrease.