Identification of the critical angle between fiber and crack direction in orthotropic materials for avoiding catastrophic failure is necessary. Recognition of the optimum regions for creating notches in orthotropic materials for creation of maximum load-bearing capability is an important parameter in structural design. In this paper, the critical angles between crack and fiber direction are predicted, extracting crack tip parameters in orthotropic materials using stress series expansion and numerical method. The variations of crack tip parameters with respect to the angle between crack and fiber for modes I and II are presented. The presented functions for these variations can be used in the optimum design procedure of orthotropic structures. The obtained results are validated using experimental study.