In this paper it is postulated that the elastic constants of anisotropic cancellous bone can be accurately predicted by its structural density and a tensoral measure of anisotropy called fabric. Orthotropic elastic moduli, shear moduli, structural density, and fabric components were measured for eleven cancellous bone specimens from the bovine femur and for 75 specimens from three human proximal tibias. The measured elastic constants were correlated to structural density and fabric components using a least squared analysis. Functions of structural density and fabric explained between 76 and 86 percent of the variance in the elastic constants. Models with squared functions of structural density proved to predict the elastic constants within the physiological range better than those with linear or cubed functions of structural density