Thermal barrier coatings (TBCs) are known to spall as a result of the residual stresses that develop during thermal cycling. TBC's are multi-layered coatings comprised of a metallic bond coat, thermally grown oxide and the ceramic top coat, all on top of a Ni-base superalloy substrate. The development of residual stresses is related to the generation of thermal, elastic and plastic strains in each of the layers. The focus of the current study is the development of a finite element analysis (FEA) that will model the development of residual stresses in these layers. Both interfacial roughness and material parameters (e.g., modulus of elasticity, coefficient of thermal expansion and stress relaxation of the bond coat) play a significant role in the development of residual stresses. The FEA developed in this work incorporates both of these effects and will be used to study the consequence of interface roughness, as measured in SEM micrographs, and material properties, that are being measured in a parallel project, on the development of these stresses. In this paper, the effect of an idealized three-dimensional surface roughness is compared to residual stresses resulting from a grooved surface formed by revolving a sinusoidal wave about an axis of symmetry. It is shown that cylindrical and flat button models give similar results, while the 3-D model results in stresses that are significantly larger than the stresses predicted in 2-D.