Radionuclides escaping from a repository in crystalline rock for spent nuclear fuel will migrate with the seeping water in the fissures. Most radionuclides will be retarded by sorption on the rock surfaces and by diffusion into the rock matrix. Available surface for sorption and residence time are two prime variables which influence the radionuclide movement. The water velocity may vary very much along a flow path, especially if the flow path enters a strongly fissured zone (lineament). In this paper the radionuclides in a stream tube with an arbitrary velocity along the flow path have been investigated, and a numerical scheme based on the integrated finite difference method (IFDM) is proposed for practical calculations. The transport mechanisms considered are advection and longitudinal dispersion and the retardation mechanisms used are instantaneous sorption in a portion of the rock (surface sorption) and diffusion into the rock matrix and sorption on the micropore surfaces. An attempt is also made to account for blocks of various sizes and shapes in introduction of a “pseudobody.” This method accounts for the large sorption surface but small volume of small blocks and small surface area but large volume of large blocks. Any block size didtrubution can be handled.