High-temperature processing induces large internal stresses at room temperature in composites because of the di erence between the thermal coe cients of the matrix and of the reinforcing particles. In this work we develop a theoretical scheme to calculate the strains in the particles by using the Eshelby equivalent method. The interaction between the inhomogeneous inclusions (® bres) is evaluated by means of a mean-® eld model given by Mori and Tanaka, and full anisotropy of ® bres and matrix is taken into account within an explicit approach by which the problem is solved as a function of the deformation ® eld instead of the thermoelastic properties. The model is applied to the thermoelastic moduli and residual stresses in biphase composites. We analyse the in¯uence of the orientation distribution function of ® bres, its volume fraction and elastic inhomogeneity factor on Young' s modulus, Poisson' s ratio and the thermal coe cients. We calculate the thermal residual stresses in an Al 2 O 3 -SiC composite as a function of direction, and the results are compared with the neutron measurements made by Majundar et al. As the non-uniform crystal structure of SiC whiskers complicates the interpretation of experimental data collected from whisker-reinforced composites, a general equation based on the fractions of cubic and hexagonal polytypes is incorporated in the model. We demonstrate that the residual stresses cannot easily be explained on the basis of elastic interactions and distribution of ® bre orientations, even accounting for the elastic and thermal anisotropy of ® bres. Correct interpretation and comparison of residual stresses with the measured values requires analysis of the peak shift and broadening stemming from the residual stresses. §1. IntroductionIn the past two decades, there has been increased interest in strengthening and toughening polycrystalline ceramics by the incorporation of ® bres and particles within the microstructure. The addition of ® bres to a ceramic or metal matrix makes it possible to enhance both the mechanical and thermal properties of the resulting composite. These properties will depend on the relative sti nesses (elastic inhomogeneity factor) and thermal moduli (thermal inhomogeneity factor) of the matrix and of the ® bres, and on the volume fraction, geometry and distribution of