This work is devoted to the numerical simulation of flows in partially saturated porous media. We describe the Richards equation governing the subsurface flow and discuss its range of applicability. A discontinuous Galerkin formulation is used to approximate the steady-state Richards equation. To this end, we present the mathematical framework and a procedure for solving the nonlinear equation. Numerical tests are carried out to highlight properties of the discontinuous Galerkin method and a test case is compared to experimental data to validate the model.