Recently a new three-dimensional fracture model has been developed in the context of the combined finite-discrete element method. In order to provide quantitative guidance for engineering applications, mesh size and orientation sensitivity are investigated by specially designed numerical tests. The mesh size sensitivity is analysed by modelling a single tensile fracture propagation problem and three-point bending tests using a series of models with the same geometry but different structured mesh sizes. The mesh orientation sensitivity is investigated by diametrically compressing a disc specimen of unstructured meshes from different angles. The computational efficiency of the three-dimensional fracture model is also studied.