Analytical models based on force and moment balances have been developed to predict the distribution and magnitude of thermal residual stresses within the multilayer coatings with graded properties and compositions due to differential thermal contraction. The closed-form solutions of residual stresses related to the material combination and the compositional gradient of coating were obtained. Specific analyses were made on the thermal residual stresses within ZrO2Y2O3/NiCrAlY functionally and compositionally graded thermal barrier coating systems. Systematic studies were conducted on the effects of the gradient exponent, the elastic modulus of ceramic component, the number of coating layers and the material properties of the substrate on the magnitude and distribution of the residual stresses within the functionally graded coating. It was found that the residual stress distribution within a functionally graded coating could be adjusted by controlling the compositional gradient or selecting a proper gradient exponent of the coating. As for the compositionally graded coating, some results similar to those for the functionally graded coating with 50 graded layers were obtained. The remarkable difference was that the thermal residual stresses were continuously changed from the substrate/coating interface to the coating surface in compositionally graded coatings, while these stresses were stepwise in functionally graded coatings. The effect of coating thickness on the residual stresses within the compositionally graded coating was also discussed. (c) 2005 Elsevier B.V. All rights reserved.