A numerical method to derive approximate solutions for stress intensity factors for rectilinearly anisotropic bodies without resolving to complex variable approach is presented. The method is based on the assumption that the crack opening profile can be simulated by a simple curve such as an elliptic function and a relationship is found for the stress intensity factor in terms of near tip displacements. An example solution is derived for a transversely isotropic body and the results are verified with Westergaard’s stress function approach. The proposed model has a great potential for the applications to fracture mechanics of anisotropic rock materials.