Fractures in the Earth's subsurface have a strong impact in many physical and chemical phenomena, as their properties are very different from those of the surrounding rocks. They are generally organized as multi-scale structures, which can be modeled by Discrete Fracture Networks (DFNs) that may contain hundreds of thousands of ellipses in the tridi-mensional space. This paper presents our approach to generate meshes of such large DFNs and to simulate single-phase flow problems using these meshes.