Functionally graded materials offer potential as a solution to the premature failure of thermal barrier coatings due to thermal residual stresses, however this solution has not been fully evaluated to date. An analytical methodology based on the bending of plates has been used to model the residual stress distribution through the layers of a functionally graded (FG) cermet top coat-bond layer-substrate system after cooling from a high deposition temperature. The model is then applied to two material systems with different trends in variation in the coefficient of thermal expansion from the substrate to the top coat layer. Increasing the number of layers reduces the discrete stress variations across the interfaces through the FG layers and reduces the propensity of interfacial cracking. While the stress in the top coat is always compressive for the Inconel substrate, the stress in the top coat is tensile in nature for the steel substrate when the ceramic volume fraction in the functionally graded layers is low. The stress in the top coat gradually becomes compressive with an increasing volume fraction of ceramic in the functionally graded top coat. The curvature of the TBC system follows a similar trend and changes its sign with increasing ceramic content for the steel substrate. The effect of the number of layers on the curvature gradually diminishes and the curvature becomes constant beyond only a few layers. © 2018