[en] The permeation rate of D₂ through 304 and 304L stainless steel for driving pressures 10^-5 to 10^-1 Pa (10^-7 to 10^-3 torr) were measured over the temperature range 650 to 1050⁰K. Two 51 mu m and one 127 mu m, 304 samples and one 127 mu m, electropolished 304L sample were studied. The steady-state permeation rate varied linearly with p/sup ¹/₂/ in the 10^-2 to 10^-1 Pa range but had a higher dependence below 10^-3 Pa. The steady-state and transient data at 10^-1 Pa were used to calculate the permeability phi = 1.9 x 10¹⁵ exp (-6300 T^-10K) molecules D₂ cm^-1 sec^-1 Pa/-¹/₂/ and the diffusion coefficient D = 3.5 x 10^-4 exp (-5100 T^-10K) cm² sec^-1. The processes involved in permeation are discussed and time-dependent formulae for the permeation rate are given for a number of simple cases. Following thermal permeation experiments, permeation rates resulting from bombardment with a 10 mu amp, 15 keV deuteron beam were measured. A high transient permeation rate was observed which is attributed to a surface impedance to reemission which decreases under bombardment