Ceramic materials applied by air plasma spray are used as components of thermal barrier coatings. As it has been found that such coatings also dissipate significant amounts of energy during vibration, they can also contribute to reducing the amplitude of resonant vibrations. In order to select a coating material for this purpose, or to adjust application parameters for increased dissipation, it is important that the specific mechanism, by which such dissipation occurs, be known and understood. It has been suggested that the dissipative mechanism in air plasma sprayed coatings is friction, along interfaces arising from defects between and within the “splats” created during application. An analysis, similar to that for the dissipation in a lap joint, is developed for an idealized microstructure characteristic of such coatings. A measure of damping (loss modulus) is extracted, and the amplitude dependence is found to be similar to that observed with actual coating materials. A critical combination of parameters is identified, and variations within the microstructure are accounted for by representing values through a distribution. The effective or average value of the storage (Young’s) modulus is also developed, and expressed in terms of the parameters of the microstructure. The model appears to provide a satisfactory analytical representation of the damping and stiffness of these materials.