In view of the laboratory tests performed at PSI with a Nafion tubular membrane reactor module for the catalysed methanol synthesis with CO2 and H-2 at 200 degrees C, the mechanical stability of a commercially available Nafion hollow fiber was tested at elevated temperatures (T=160-200 degrees C) and pressures (P<30 bar). To this end, a single fiber (wall thickness approximate to inner radius approximate to 65 mu m) was installed in a bent stainless steel tube and heated in an oil bath. Pressurised air was used to create mechanical stress on the fiber's outside, while leading atmospheric nitrogen gas through the inside. The nitrogen flow rate was found to converge steadily towards a lower steady value, the value of which decreased systematically with increasing temperature and pressure difference (Delta P) across the fiber wall surface. The steady flow rates are attributed to changes in the inner fiber radius and interpreted using Poiseuille's formula. The steady how rates were obtained with one and the same fiber as Nafion exhibits visco-elastic properties at these elevated temperatures which allows dimensional regeneration under unstressed conditions (Delta P=0). At temperatures around 160 degrees C we estimate that a Delta P of 25 bar is permissible; under the minor penalty that the fiber radius will shrink by ca, 10% maximally. At 200 degrees C we expect material failure for Delta P beyond 5 bar as the fiber collapses irreversibly. Model analysis of the applied stress as a function of the radial fiber dimensions reveals that the maximum Delta P advisable (at given temperature) can be raised by 45% when using Nafion fibers with a fourfold smaller inner radius with the high pressure side on the inside.