Experimental measurements of the isotropic elastic moduli on polycrystalline specimens of hydroxyapatite and fluorapatite are compared with elastic constants measured directly from single crystals of fluorapatite in order to derive a set of pseudo single crystal elastic constants for hydroxyapatite. The stiffness coefficients thus derived are: c₁₁ = 13.7, c₁₂ = 4.25, c₁₃ = 5.49, c₃₃ = 17.2, and c₄₄ = 3.96 (all in 10ⁱⁱ dyn/cm²). Anisotropic and isotropic elastic properties are then computed and compared with similar properties derived from experimental observations of the anisotropic behavior of bone.