The rate of rise method was arranged for monitoring the kinetics of hydrogen evolution from austenitic stainless steel (AISI 304) samples, inductively heated in the range from 300 to 1000 degreesC. After each heating cycle, the accumulated gases were analyzed by quadrupole mass spectroscopy and quantity of evolved hydrogen was determined. Three sample types were studied: "only cleaned,'' hydrogen annealed (1050 degreesC), and vacuum annealed (950 degreesC). Below 800 degreesC, the effect of pretreatment was manifested very differently in kinetics. Fast release of approximately 2 x 10(19) atoms H cm(-3) from hydrogen annealed samples was recorded which was close to published data of solubility. By increasing the temperature above 800 degreesC for a prolonged time, much more hydrogen evolved from all sample types. The equivalent concentration change varied from 4 to 9 x 10(19) atoms H cm-3, but the measurements were ceased before the ''totally outgassed state'' was reached. By repeated annealing of two samples in high vacuum, the rest of the hydrogen was again partially extracted and partially redistributed to the sites, from which it was easily released after intermediate cooling down. There is a lack of data in the Literature about the amount and evolution kinetics of the trapped or tightly bound hydrogen. The present findings differ from existing theoretical models of outgassing and may explain the reason for the inefficiency of thermal treatment methods to prepare stainless steel for extreme high vacuum application.