Based on the asymptotic crack tip characteristics of anisotropic elasticity, a moving template finite element simulation scheme is developed to establish the stress intensity factors of multiple cracks in materials with directionally dependent mechanical properties. This is achieved from a hierarchical point of view wherein a global finite element model is recursively used to obtain the boundary condition information (deflections/forces) for the templates, i.e. 2nd level finite element mesh attached to the various cracks associated with a given structure. The many crack wakes in the global model are defined through the use of birth and death elements which are themselves handled hierarchically. The individual templates are solved separately so that their associated embedded singularities can be employed to determine local crack tip physics. The procedure provides the capability to handle both directional stiffness, strength and fatigue property variations. This is achieved by reinterpreting the tip physics from a probabilistic point of view. The result is a new scheme to define cracking directionality. Overall, the procedure provides such information as the mean cracking direction, as well as higher order probabilistic properties, the standard deviation, skewness, multimodality, kurtosis, i.e. lepto/platekurticity and so on. Due to the generality of the moving scheme, propagating multiple cracks can be simulated along with their joint interactions/shading effects. To demonstrate the scheme, several example problems are included. These both illustrate the effects of material anisotropy, as well as benchmark the procedures overall accuracy in correlations with available simulations.