The widely different uses of geomembranes as barriers to the transport and migration of different gases, vapors, and liquids under different service conditions require a determination of permeability by test methods appropriate to the service. Geomembranes are nonporous and homogeneous materials that permeate gases, vapors, and liquids on a molecular scale by dissolution in the geomembrane and diffusion through the geomembrane. The rate of transmission of a given species, whether as a single permeant or in mixtures, is driven by its chemical potential or concentration gradient. Various methods to assess the permeability of geomembranes to single component permeants, such as individual gases, vapors, and liquids are described and data are presented. In addition, various test methods for the measurement of permeation and transmission through geomembranes of individual species in complex mixtures such as waste liquids are described and data are presented.