The work presented here experimentally analyzes the compaction behavior of a thin graphite facing gasket material utilizing a new patented lateral displacement fixture. Two constitutive relationships are presented to describe the measured material characteristics, using this new fixture system. The first approach is a more conventional method of taking the load-deformation curve of the material to analyze the stress-strain relationship. The second approach develops the stress-strain relationship using a soils model. The soils model relates the true axial stress to the volumetric strain. The constitutive relationships account for thickness, shape, and surface friction condition variations of the material. To study these variabilities, three thicknesses, two diameters, and two surface friction conditions were considered.