We studied the influence of tectonic perturbations on the transport of potentially mobilized radionuclides in groundwater from a deep-mined repository of solid high-level radioactive waste. The study was carried out by the method of mathematical modeling. Key parameters of the model correspond to the site of a potential federal repository in Russia. The groundwater flow domain is delimited on one side by a water divide (i.e., boundary of the catchment basin) and on the other side by the river bank. 2D simulations of groundwater flow and radionuclide migration are carried out along a vertical cross-section normal to the water divide. The groundwater flows through the rock massif, which encloses the repository, and discharges into the adjacent river. It is supposed that tectonic activity may form a fault which is parallel to the river bank. We analyzed how repository safety depends on the time of the fault emergence and on the distance between the repository and the fault. The results of our simulations suggest that: (1) emergence of a fault due to tectonic perturbations is not inevitably associated with a substantial growth of radionuclides released from the repository to the environment; (2) influence of the fault on the repository safety depends on the distance between the fault and the repository as well as on the time interval between the repository development and the fault emergence; (3) the influence of the fault on the repository safety can depend substantially on local elevations of the relief at the repository site.