The migration of radionuclides in the fissures in the bedrock surrounding a repository is discussed. A one-dimensional transport model is presented. It includes diffusion of the nuclides into the microfissures of the rock, and linear sorption, and longitudinal dispersion in the bedrock. An analytical solution to the model is given in terms of an infinite integral. The integrand is a sometimes highly oscillatory function of the system parameters. A special integration method is developed to evaluate the infinite integral. The method utilizes the oscillatory behavior of the integrand. The assessment of input parameters is discussed in some detail. Dimensionless breakthrough curves are given for the approximate range of variation of the input parameters. Calculations are made for a repository of spent fuel surrounded by fissured but fairly good rock (Kp = 10-9 m/s and fissure spacing S = 50 m). Longitudinal dispersion may significantly affect the amount of radioactive material reaching the biosphere. Radionuclides, which would decay completely without longitudinal dispersion, may arrive in nonnegligible concentrations. Dispersion effects of the magnitude considered in this study can significantly diminish the retardation effects of matrix diffusion.