Since rocks generally are brittle materials, the generating, propagating, and combining of cracks in rocks play an important roles in the failure progress of rocks . Many researchers have concluded that the crack pattern have fractal properties, and the fractal method can be used to analyze the failure of rock. In this article, the box fractal dimension of two kinds of rock has been measured based on an experiment of SEM. The results illustrated that fractal dimension values varied with rocks. By numerical methods , the mechanism of the variation and relation to the stress and mineral composition in rocks have been studied. Further more, the failure properties characterized by the variation of fractal dimension are also studied by energy method.