The objective of this study was to investigate thermal stresses in oxidation protection coatings on carbon-carbon composites. Multilayer coatings with each layer of coating applied at a different temperature, and gradient coatings with continuously varying properties through the thickness of the coating were considered. Particular emphasis was on the prediction of the thermal stresses in the vicinity of geometric discontinuities. For the analysis an incremental generalized plane-strain finite element model that accounts for temperature-dependent material properties and continuously varying properties in the gradient coatings was developed. The model is based on an incremental constitutive equation for linear thermoelastic materials that accounts for the coupling between stresses and the temperature-dependence of the material properties. In addition to the finite element model, an incremental simplified plane stress analysis for the prediction of stresses away from geometric discontinuities was developed. Analyses of carbon-carbon substrates with coatings showed that large stress concentrations in the coatings may be present near the geometric discontinuities. It was found that inserting a compliant layer between the carbon-carbon substrate and the oxidation protection coatings, or inserting a gradient coating with properties varying from those of a compliant material near the carbon-carbon substrate to those of the oxidation protection coating near the oxidation protection coating, could be used to significantly reduce the magnitudes of the stresses in the stress concentrations. The influence of geometric and material parameters on the stresses was studied and for some combinations of parameters stresses near the geometric discontinuities could be reduced to magnitudes that were smaller than the magnitudes of the stresses away from the discontinuities. For coatings applied at different temperatures, the application temperature of the coatings significantly influenced the magnitude of the stresses. The lowest stresses were obtained for gradient coatings for which the application temperature of the gradient coating varied continuously, proportional to the material composition in the gradient coating. / Ph. D.