Directionally solidified mullite fibers have been grown by the laser-heated, float-zone method from starting materials with a nominal composition of 3Al(2)O(3).2SiO(2). The fibers used in this study have large single-crystal regions with composition 2.5Al(2)O(3).SiO2 and [001] fiber axis orientation. The complete elastic tensor of these samples has been determined by Brillouin spectroscopy at room temperature and elevated temperatures up to 1200degreesC. Isotropic moduli (bulk, shear, and Young's) have been calculated using the Voigt-Reuss-Hill averaging scheme. The room-temperature values obtained are K-VRH = 173.5 +/- 6.9 GPa, G(VRH) = 88.0 +/- 3.5 GPa, E-VRH = 225.9 +/- 9.0 GPa. All moduli show gradual, linear decreases with temperature. The temperature derivatives obtained for the equivalent, isotropic moduli are dK(VRH)/dT = - 17.5 +/- 2.5 MPa/degreesC, dG(VRH)/dT = -8.8 +/- 1.4 MPa/degreesC, dE(VRH)/dT = -22.6 +/- 2.8 MPa/degreesC. Substantial differences between bulk properties calculated from the single-crystal measurements in this study and the properties reported in the literature for polycrystalline sintered mullite are identified, indicating the importance of factors such as microstructure, intergranular phases, and composition to the elasticity of mullite ceramics.