This paper evaluates the stress intensity factors (SIFs) at the crack tips, predicts the crack initiation angles and simulates the crack propagation path in the two-dimensional cracked anisotropic materials using the single-domain boundary element method (SDBEM) combined with maximum circumferential stress criterion. Numerical examples of the application of the formulation for different crack inclination angles, crack lengths, degree of material anisotropy, and crack types are presented. Furthermore, the propagation path in Cracked Straight Through Brazilian Disc (CSTBD) specimen is numerically predicted and the results of numerical and experimental data compared with the actual laboratory observations. Good agreement is found between the two approaches. The proposed BEM formulation is therefore suitable to simulate the process of crack propagation. Additionally, the anisotropic rock slope failure initiated by the tensile crack can also be analyzed by the proposed crack propagation simulation technique.