In the frame of the FAIR project irradiation test of superconducting magnet components was performed at GSI Darmstadt in May 2008. As a part of the experiment stainless steel samples were irradiated by 1 GeV/u 238 U ions. In contrast to the previous experimental studies performed with thick cylindrical samples, the target was a thin plate irradiated at small angle. The target was constituted as a set of individual foils. This stacked-foil target configuration was foreseen for depth-profiling of residual activity. Gamma-ray spectroscopy was used as the main analytical technique. The isotopes with dominating contribution to the residual activity induced in the samples were identified and their contributions were quantified. Depth-profiling of the residual activity of all identified isotopes was performed by measurements of the individual target foils. The characteristic shape of the depth-profiles for the products of target activation and projectile fragments was found and described. Monte Carlo code FLUKA was used for simulations of the residual activity and for estimation of the number of ions delivered to the target and their distribution. The measured data are relevant for assessment of radiation situation at high-energy accelerators during the "hands- on" maintenance as well for assessment of the tolerable beam-losses.