The activation of structures and surroundings of new high-intensity heavy-ion accelerators like the Facility for Antiproton and Ion Research (FAIR) is an important issue. Monte Carlo codes such as FLUKA allow the prediction of the production of individual radioactive isotopes and the induced radioactivity that causes the main contribution to the radiation exposure of personnel. The work is a benchmark study of activation predictions for uranium beams with 500 and 950 MeV/u deposited in copper and stainless steel targets. Precise gamma spectrometry measurements for isotope identification have been carried out with a HPGe detector. All gamma-emitting radionuclides with half-lives of more than 2 days that contribute significantly to the residual dose rates have been studied. The benchmark study shows that FLUKA is a suitable code for the prediction of induced radioactivity at medium-energy heavy-ion accelerators.