Abstract: The Generalized Integral Transform Technique (GITT) was employed to simulate transient one-dimensional flow in variably saturated porous media, as well as radioactive waste transport within different layers (a solid waste pile, nearby soil, and a granular aquifer) towards the edge of a uranium mining installation under institutional control. Computational codes, written using the Mathematica software system, were implemented and tested for solution of the coupled advection-dispersion equations for an arbitrary number of daughter products within a radioactive chain migrating in saturated and unsaturated soil layers. The computer simulations were verified in great detail against results obtained using the built-in routine NDSolve of the Mathematica platform and the HYDRUS-1D software system. The present work reports the main results for 238U chain radionuclide transport using data extracted from a safety assessment of solid waste repositories at a uranium mining and milling installation in Caetité, state of Bahia, Brazil, operated by INB (Indústrias Nucleares do Brasil). Concentration evolutions of the various radionuclides obtained with the simulations were analyzed for five different cases to explore variations in the infiltration and recharge rates, the effect of assuming physical equilibrium or non-equilibrium transport conditions, and of different initial concentrations of some of the radionuclides.