<p>Residual stresses arise in ceramic/metal interpenetrating phase composites because of non-equal thermal shrinkage of the metal and ceramic phases when cooling from the manufacturing temperature to the ambient one. Experiments on hot pressing bi-material samples have shown perfect compatibility between alumina Al₂O₃ and a Ti alloy and Al₂O₃ and Mo explained by a low mismatch in thermal expansion in these pairs. Debonding is observed between a porcelain and a CoCr alloy with a considerable mismatch in thermal expansion. A thermoelastic computational model is developed for periodic ceramic/metal composites. Numerical simulation reveals generally tensile stresses in the ceramic phase and generally compressive stresses in metal in Al₂O₃/Mo composites where thermal expansion of metal is lower than that of ceramic. On the contrary, compressive stresses in the ceramic phase and tensile stresses in metal arise in Al₂O₃/Ti and porcelain/CoCr composites where thermal expansion of metal is greater than that of ceramic. Debonding forces can be avoided on the porcelain/CoCr interface by optimizing composite geometry and ceramic/metal ratio. However, considerable shear stresses can still result in destruction of the ceramic phase.</p>