Currently, the storage of ore processing residues is a major challenge in the mining industry. These tailings are increasingly filtered in advance of disposal using filter presses to make storage safer and to recover water effectively. However, the falling of the detached filter cakes between the individual filtration cycles results in the abrasive wear of the filter cloths at specific points of the chamber geometry and is a main reason for the necessity of a regular replacement. Improved filter media selection through abrasion testing replicating this specific load case increases plant economics by reducing the risk of unplanned downtimes. Therefore, this article explains a test procedure adapted to the direction-specific wear. A brush apparatus is presented, which abrasively loads filter fabrics stretched over an exchangeable edge geometry uniaxially in one direction. The effects of important apparatus setting parameters (sample clamping torque, brush overlap, and brush speed) are shown. Furthermore, the resistances of three different filter media typical for tailings filtration were compared and different edge geometries investigated. Thereby, significant differences were found with regard to filter media type, filter media material, and edge geometry. Depending on the edge geometry used, the polypropylene fabric withstands a load amount by a factor of 3.3 to 8.9 higher than the nonwoven polypropylene, the nylon fabric withstands a load amount by a factor of 3.6 to 5.3 higher than the polypropylene fabric and the nylon cloth withstands a load amount by a factor of 16.1 to 31.8 higher than the nonwoven polypropylene.