A mathematical model of the diffusion of radionuclides through engineered safety barriers is developed for 14C in order to determine the long-term safety conditions and characteristics of a decommissioned commercial uranium-graphite reactor. Dry and wet mixtures and concrete are used as the barrier materials. Diffusion is studied as the dominant mechanism for the transport of the radionuclides. The 14C concentration at the boundary between the radwaste storage site and the environment is determined computationally and the effect of the modeling conditions on the specific activity of the radionuclide is analyzed. The decomposition sequence of the safety barriers for which the 14C concentration is much lower than the admissible value is determined.