The prediction of flow behavior and pressure drop in fibrous filter media is challenging due to the complexity of the nonuniform fiber structure. Numerical calculation tools can considerably contribute to pressure drop determination for inhomogeneous filter structures. A numerical solution approach based on the finite element method to simulate 2D and 3D filter structures is considered. As numerical examples, computer designed homogeneous and inhomogeneous 2D cases where the numerical approach is validated by analytical models are investigated. Furthermore, the capability of the numerical method to simulate real 3D structures corresponding to more than 25 million degrees of freedom of the related algebraic system is demonstrated. The large systems involved require the use of dedicated techniques related to high performance computing.