In this paper, a ring shaped numerical specimen is used to studying the failure process in brittle materials. The ring specimen is subjected to a compressive diametral load and contains two angled central cracks. Numerical modeling in this study is performed. It is shown that the obtained numerical results are in a very good agreement with the experiments. Effect of the crack orientation angle on the failure modes and loading-displace responses is discussed. In the range of 0°~40°, the fracture paths are curvilinear forms starting from the tip of pre-existing cracks and grow towards the loading points. For the crack orientation angle 90°, vertical fractures will split the specimen and the horizontal cracks do not influence the fracture process.