To improve the understanding of gas transport processes in tight rocks (e.g., shales), systematic flow tests with different gases were conducted on artificial micro- to nanoporous analogue materials. Due to the rigidity of these systems, fluid-dynamic effects could be studied at elevated pressures without interference of poro-elastic effects. Flow tests with narrow capillaries did not reveal any viscosity anomaly in a confined space down to capillary diameters of 2 µm. Experiments with nanoporous ceramic disks (> 99% Al2O3) conducted at confining pressures from 10 to 50 MPa did not indicate any stress dependence of permeability coefficients. Analysis of the apparent permeability coefficients over a mean gas pressure range from 0.2 to 30.5 MPa showed essentially linear Klinkenberg trends with no indication of second-order slip flow. The Klinkenberg-corrected permeability coefficients measured with helium were consistently higher than those measured with all other gases under the same conditions. This “helium anomaly” was, however, less pronounced than the same effect observed in natural rocks, indicating that it is probably not related to fluid-dynamic effects but rather to gas–solid interactions (e.g., sorption). Permeability tests with CO2 on the nanoporous membrane show significant deviations from the linear Klinkenberg trend around the critical point. This is due to the drastic changes of the thermodynamic properties, in particular the isothermal compressibility, in this pressure and temperature range. Helium pycnometry, mercury intrusion porosimetry and low-pressure nitrogen sorption showed good agreement in terms of porosity (~ 28%) and the most prominent pore diameter (~ 68.5 nm).