The second development of ABAQUS is implemented to simulate the initiation, propagation processes of flaws in brittle materials under compressive loading (in the paper ‘flaw’ means ‘the initial crack’, and ‘crack’ means ‘the branch crack’), by which the propagation paths and the corresponding stress intensity factors of the branch crack can be calculated. Further more the experiment is carried out to verify the validity of the above numerical method. By the numerical method, the propagation processes of open flaws and close flaws are simulated, and the comparative analysis of propagation characteristics between the open flaw and the close flaw is carried out. The results show the obvious difference in the propagation characteristics between open flaws and close flaws with the same initial flaw length and angle. Firstly, compared with the close flaw, the branch crack of the open flaw grows along a more obviously curvilinear path, and the propagation path gradually approaches to a line, which passes through the middle point of the open flaw and parallel to the maximum principal stress. Secondly in the early stage of the crack propagation, the stress intensity factors of the branch crack of the open flaw are greater than of the close flaw, but with the further propagation of the branch cracks, the stress intensity factors of the branch crack of the open flaw will be less than of the close flaw. Additionally, according to the close flaw, with the decrease of the friction coefficients, the curve characteristics of the crack propagation paths become more obvious. Therefore, it is noteworthy that the wing crack of the close flaw can be regard as the straight line if the friction coefficient of the flaw surface is very small. The above differences of the propagation characteristics between the open flaws and the close flaw show that the two flaws should be distinguished strictly in the fracture analysis.