The wall thickness of austenitic stainless steel, now in common use on vacuum chambers, is based on an overestimate of the permeation of atmospheric hydrogen through the walls. This error is based on (1) the use of data from an experiment with pure hydrogen, not atmospheric; (2) neglect of the evidence for the strong influence of oxygen and oxide layers on the reduction of permeation; (3) a simplified extrapolation procedure; (4) neglect of the change in vacuum outgassing rates due to recombination of atomic hydrogen. There has been no experimental demonstration of the existence of such permeation. The actual room temperature permeation is estimated to be less than the accepted estimate by several orders of magnitude. Thus, vacuum systems may be designed with substantially thinner walls, as thin as they can be made to withstand atmospheric pressure. These in turn, will permit much simpler outgassing procedures, and the achievement of lower outgassing rates in practice.