Recent determination of the elastic moduli of hydroxyapatite by ultrasonic methods permits a re-examination of the Voigt or parallel model of the elastic behavior of bone, as a two phase composite material. It is shown that such a model alone cannot be used to describe the behavior of bone. Correlative data on the elastic moduli of dentin, enamel and various bone samples indicate the existence of a non-linear dependence of elastic moduli on composition of hard tissue. Several composite models are used to calculate the bounds on the elastic behavior of these tissues. The limitations of these models are described, and experiments to obtain additional critical data are discussed.