The micromechanical stresses associated with hexagonal (6H) alpha-SiC platelets within a fine-grained alumina matrix were calculated using an Eshelby approach. The stresses within and around the interface of SiC platelets were determined. Both stresses were found to be strongly dependent on the morphology and the volume fraction of the SiC particles. The morphology effect, however, tended to be limited at aspect ratios greater than or equal to 10. Owing to anisotropy in the thermal and elastic properties of alpha-SiC, the residual stresses just outside the inclusion also depended on the position along the SiC/Al2O3 interfaces. The maximum tensile stress was found at the edges of SiC platelets. There were two principal tangential tensile stresses which differed greatly at the edges of disc-shaped inclusions. The results of the stress analysis were consistent with observed differences in microcrack morphology and the resultant reduction of the Young’s modulus of the composites.