Good mechanical properties and chemical stability at high temperatures make silicon nitride a good candidate as an advanced engine material. Much research has been done to characterize the mechanical strength and resistance of crack propagation in this material. In this paper, we use fractal analysis to study the geometry of Si3N4 fracture and wear surfaces. We found that the geometries of the failure surfaces as characterized by the fractal dimensional increment, D*, under different failure stress states are similar for the same brittle material, but different for different brittle materials. The similar D* in an identical brittle material implies that the failure process in the material is the same regardless of loading mode, i.e., mode I or mixed-mode stress. The fractal technique is shown to be useful for correlating the fractal dimension to the material properties and fracture-surface topography.