Accurate simulation of crack propagation paths in engineering materials is what designers and engineers are always looking for. An important element of any simulation package is to define a criterion for crack initiation angles. Many criteria have been proposed to predict crack initiation angles under mixed mode loading. Most of them assume either a constant radius or a Mises type variable radius for the core region at the crack tip. In a recent study, we presented a detailed analysis of the core region and showed strong dependence of mixed mode crack initiation angles on the shape of the core region. In addition, we proposed a criterion based on the shape of the crack tip core region for isotropic materials. Since most engineering materials are anisotropic, it is necessary to modify the criterion developed for isotropic materials. In this study, we investigate the shape of the core region at the crack tip in mixed mode loading for anisotropic materials under different loading conditions. We employ isotropic linear elastic stress field along with Hills anisotropic yield criterion at the crack tip and examine the effect of anisotropy on the shape of the core region and its relation to crack initiation angles.