In this study, we present an analysis of the internal stresses generated during cooling of alumina-chromium composites using a micromechanical approach by a finite element method. Residual stress fields are calculated for microstructural models derived from a scanning electron microscope image. Results show in particular that particles with concave shapes can generate relatively high local plastic deformation and residual stress distributions in the adjacent matrix that are very different from those of particles with a spherical shape. We present also the experimental determination of residual stresses using synchrotron radiation from LURE. We show that measurements are possible and the results concerning the mean stresses in the alumina and chromium phases are analyzed.