Anisotropy is an essential attribute exhibited by most biological materials. Based on the recent work on anisotropy of a wide range of crystals and polycrystals, we propose an appropriate measure (A) to quantify the extent of elastic anisotropy in biomaterials by accounting the tensorial nature (both stiffness-based and compliance-based) of their elastic properties. Next, we derive a relationship between A and an empirically defined existing measure. Also, the preceding measure is used to quantify the extent of anisotropy in select biological materials that include bone, dentitional tissues, and a variety of woods. Our results indicate that woods are an order of magnitude more anisotropic than hard tissues and apatites. Finally, based on the available data, it is found that the anisotropy in human femur increases by over 40% when measured between 30% and 70% of the total femur length.