One of the prime motives for studying the elastic properties of the apatites stems from the occurrence of hydroxyapatite, OHAp, in calcified tissue. In this paper the isotropic elastic contents of crystalline apatite solids are determined from measurements of elastic wave velocities through powders under pressure. Once obtained, these elastic constants are used to model the elastic behaviour of a two-phase composite material having one phase more rigid than the other by a factor of 2.4. The results are then used in a general discussion of the probable order of magnitude of the elastic constants of the organic non-crystalline phase in bones and teeth, under the assumption of a two-phase system.