In solid rock aquifers low matrix permeability is often accompanied with fractures and faults of different scales. Therefore, numerical modeling of such coupled systems is very complex. Flow of groundwater and mass transport processes in fractured systems have to be modeled along discrete surfaces joined to the common matrix representation. This leads to high demands on the quality of finite element mesh generation. Another difficulty is the evaluation of field parameters needed in the design of realistic models to simulate natural systems. This paper presents a strategy to generate three dimensional finite element meshes, which allows the modeling of groundwater flow and contaminant transport in a coupled matrix fracture aquifer system. Software development and data evaluation for the discussed application example comes from the research project “Development and Application of Analytical Methods on Investigations of the Reliability of Disposals in Open Mines” sponsored by the German Ministry of Education and Research. The scope of this project is to determine the influence of a rising groundwater level in closed coal mines on the transport of contaminants from waste material deposits in cut coal seams.