The calculation of the scalar compressive and shear anisotropy factors developed for single crystal refractory compounds has been adapted to the anisotropic elastic stiffness coefficients determined by a number of ultrasonic measurements of bone based on transverse isotropic symmetry. Later, this work was extended to include the ultrasonic measurements of bone based on orthotropic symmetry. Recently, the five transverse isotropic elastic constants for both wet and dry human dentin were determined using resonant ultrasound spectroscopy. The five transverse isotropic elastic constants for wet bovine enamel and dentin had been calculated based on modeling of ultrasonic wave propagation measurements and related data in the literature. The scalar compressive and shear anisotropy factors have been calculated from both these sets of data and are compared with a representative set from those published previously for both human and bovine bone and both fluoro- and hydroxyl-apatites.