Propagation of high-energy (above 20 MeV) nuclear data uncertainties on the safety related neutronic responses in accelerator driven systems has been assessed. The total core power and production of radionuclides contributing to radiation source terms were focused on. The article features a method based on the Monte Carlo sampling of random nuclear data files from the covariance matrices generated from the sets of reaction cross sections obtained with model calculations of high-energy particle interactions with matter or picked up from already existing nuclear data libraries. It has been demonstrated that nuclear data uncertainties do not need to be propagated through particle transport calculations to obtain uncertainties on the responses. This advantage allowed to investigate the convergence of the sample average to the best estimate. The number of random nuclear data file sets needed to obtain reliable uncertainty on the total core power is around 300 that results in the uncertainty of 14%. The uncertainties on the concentrations of nuclides most important for the safety assessment that are accumulated in lead–bismuth eutectic during irradiation, range from 5 to 60%. Concentrations of some nuclides exemplified by Tritium converge much slower than neutron multiplicities so that several thousands of samples are needed to ensure reliable uncertainty estimates.