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Increasingly, thermal interstitial materials (TIM), such as metallic foils, solder, metallic coatings, polymeric matrices loaded with highly conducting filler particles (i.e., elastomers), greases, and phase-change (PCM) materials are being employed to a greater extent in power generating systems. With greater use, follow an increased interest in the thermal transport and mechanical properties of these materials. These properties include thermal conductivity, thermal diffusivity, Young's modulus, Poisson's ratio, and the thermal resistance at the interface between the interstitial material with the substrate material. To provide information on the thermal joint conductance of an important interstitial material employed in microelectronic components, an experimental investigation has been conducted for flexible graphite. The experimental data were compared to an analytical model developed for elastic layers. The model and data are found to be in good agreement over the pressure range within the investigation. The proposed model can be used to predict the lower bound on the joint conductance.