Given the diminishing non-renewable energy resources and limited progresses achieved in the renewable energy sectors in India, the existing data projects that nuclear power can play a significant role in sharing the burden of meeting the growing energy demand. Low-, medium-, and high-level radioactive wastes generated from such nuclear power plants are to be disposed safely in the subsurface geological formation with the least environmental impact. In this context, a mathematical model for describing the spatial and temporal distribution of concentration of a radionuclide chain in a saturated subsurface system is presented. The transport of radionuclides occurs by advection and hydrodynamic dispersion, while diffusive transport of radionuclides takes place from mobile into immobile water zone, in a direction, normal to the direction of fluid flow. For decay of radioactive species within fracture and rock matrix, the ingrowth of daughters is considered. In addition, unlike earlier models, the present mathematical model also takes into account precipitation and dissolution of radionuclides within high-permeable fractures and low-permeable rock matrix using first-order reaction kinetics. Further, it is also proposed that unlike dispersive-dominant sub-surface disposal of radionuclides, molecular-level surface and Knudsen diffusion play a critical role for diffusive-dominant deep geological disposal. © 2014 © 2014 Indian Society for Hydraulics.