Salt is a candidate rock to host nuclear waste repositories in many countries. Brine exists in natural salt as inclusions in salt crystals and in grain boundaries. Brine inclusions in crystals move to nearby grain boundaries when subjected to a temperature gradient, because of the temperature-dependent solubility of salt. Brine in grain boundaries moves under the influence of a pressure gradient. Brine consolidates around high-level waste packages a few years after emplacement. Heated salt near the waste package expands against the waste package and surrounding salt, creating high compressive stresses near the waste package and resulting in pressure above the lithostatic pressure. Brine pressure increases because grain-boundary brine expands more than does the salt. This increased pressure gradient causes brine to flow outward into the cooler salt. Outward flow of brine relieves the pressure gradient on the fluid, which finally relaxes to near-lithostatic pressure. Outward brine movement can become a mechanism for radionuclide transport. To determine the extent to which advection by brine in grain boundaries is an important transport mechanism for released radionuclides, it is necessary to estimate the time-dependent migration of brine. The possible role of brine migration in radionuclide transport in a nuclear waste repository is studied. Mathematical derivation of the analysis is given, along with numerical illustrations using parameter values typical of a nuclear waste repository. For heat-emitting wastes and the parameters studied here, brine migration in salt is minuscule, of the order of micrometres per year, localized within a few metres from the waste package, and highly transient, fading away within a few years of waste emplacement.