Effective elastic properties and residual stresses were assessed in directionally solidified ternary eutectic ceramic, Al2O3/YAG/ZrO2, by finite element analyses. A 3D finite element model was generated from a CT scan, representative of the microstructure and with a similar volume fraction. Effective elastic properties were calculated by numerical homogenisation. They highlight a quasi-isotropic behaviour of the ternary eutectic ceramics. Despite the difficulties to measure the strain, the dispersion observed in the results and the limited reliability of the materials properties, the results constitute a step towards a better understanding of the material behaviour. Thermal residual stresses induced by the manufacturing were also evaluated. Tensile residual stresses in yttria-stabilised zirconia and compressive residual stresses in YAG and alumina were highlighted. This evaluation also shed light on the influence of the phase morphology in the microstructure. Indeed, the computed spatial distribution of the residual stresses showed that they are different from one position to another due to the variation in phase morphology and also to material properties variability. Therefore, it is important when numerically assessing the thermomechanical properties to take into account the microstructure morphology as well as the variability of material properties.