In this work, the mechanism for fracture of brittle substances such as rocks under a uniform normal tension is considered. The oriented straight micro-cracks are mostly created in all the polycrystalline materials resulting from the stress concentrations. The present work focuses on the interactions of the pre-existing micro-cracks, which can grow and propagate within a rock-like specimen. The micro-crack initiation and propagation in rock-like specimens is investigated using the Fortran Code TDDCRACK2D, which is a 2D displacement discontinuity method (DDM) for crack analysis, a boundary element computer code based on the linear elastic fracture mechanics (LEFM) theory. In the present work, a higher order DDM is used to implement special crack tip elements for estimation of the stress intensity factors (SIFs) and crack initiation angles for the wing-crack problems initiated at different angles from the original micro-crack tips in an infinite specimen under a uniform tension.