In this paper, a new test specimen as "Center Notched Disk Tension (CNDT)" to study mode I and II stress intensity factors (SIF’s) in orthotropic materials is presented. In the field of Fracture Mechanics, mode I and II SIF’s play an important role to describe the stress distribution. In CNDT specimens, for crack along the fibers, mode mixity is created by changing the loading direction. Also, by changing the crack-fibers direction for the desired crack-load, various mode mixity can be created. For desired crack-fiber angle, by changing the loading share, different mode mixities are created. Thus, the crack kink changes the loading shares. In this analysis, a comprehensive study is performed on the influence of crack-fibers orientation and crack-loading direction on SIF’s. For the first time, SIF’s are presented for cracked orthotropic specimens in different crack-fibers and crack-loading directions. SIF’s are estimated using the Finite Element Method (FEM). The presented specimen is standardized using a unite load in different directions. The crack length is assumed to be constant. Analytical relationships are also presented for the crack tip parameters in mode I and II. Pure mode I and II conditions are investigated based on SIF’s. Due to the difficulty of establishing pure mode II conditions, it is possible to establish pure mode II conditions at certain crack-fiber and load-crack angles. In these situations, mode II SIF’s can be extracted. The obtained results are validated using reported results in the literature.