In this work, we address the issue of the sealing performance of ring-shape valve compression packings. Our analysis is focused on the characterization of the permeability of the rings made of die-formed exfoliated graphite. Because of the tight character of the material, significant Klinkenberg effects are expected. In addition, due to the manufacturing process, permeabilities kz and kr as well as Klinkenberg coefficients bz and br in the respective axial and radial directions are markedly different and strongly dependent upon the applied stress. A specific experimental device based on pressure pulse decay of nitrogen through the material was designed for the measurement in each direction under a controlled axial compression. Determination of kz and kr and bz and br is performed on the basis of a nonstationary gas flow model in the radial and axial directions using an inverse procedure applied to the pressure decay signal. Our results confirm the efficiency of the method developed here. They clearly show the anisotropic character of the material (kz is roughly one order of magnitude larger than kr) and the dependence upon axial compression. The present analysis is the key step before further quantification of the leak rate that may result from the permeation through the material as envisaged here as well as through interfaces between the housing, the packings, and the stem.