Using two theoretical models, we estimated the isotropic elastic constants of an alumina-mullite ceramic composite. The alumina phase, 20% by volume, consisted of brick-shaped particles with a 4:1 aspect ratio embedded in a mullite matrix (mullite= 3Al(2)O(3).2SiO(2)). We took alumina elastic-constant values from the literature, and we measured mullite’s elastic constants using a megahertz-frequency pulse-echo method. The two theoretical models, Datta-Ledbetter and Mori-Tanaka, proceed from very different viewpoints. The Datta-Ledbetter model uses the long-wavelength limit of a scattered plane wave ensemble-average approach. The model estimates the speed of a plane harmonic wave, averages the scattered field by the Waterman-Truell procedure and uses Lax’s quasicrystalline approximation to sum over pairs. The Mori-Tanaka method proceeds by estimating the average matrix stress in a material containing ellipsoidal inclusions. For randomly oriented ellipsoids, it extends Eshelby’s solution for a single ellipsoidal inclusion. Both models lack adjustable parameters. Surprisingly, the two models with different physical approaches give practically identical results. A rough check on our estimates is that they lead to correct predictions of the elastic constants of an alumina-mullite-particle aluminium-matrix composite.