A three-dimensional numerical groundwater contaminant transport model that can handle inhomogeneity and anisotropy is developed for the decay chain transport in groundwater from uranium tailings ponds. Initially, uranium tailings consist of the parent radionuclide ²³⁸U and its very long-lived progenies. Subsequently, ingrowths of progenies will occur in the tailings pond as well as in the groundwater during transit. Explicit finite difference method with an upwind scheme is used for solving the model equations. The model is verified using the results of analytical solutions available in the literature. Verification shows good comparison between numerical and analytical solutions for different cases. After the verification exercise, the model is applied to a hypothetical uranium tailings pond problem and the importance of the decay chain transport is highlighted. It is shown that exclusion of the decay chain transport underestimates the radiological impact of uranium tailings ponds almost by a factor of 100. It is observed that ²²²Rn, ²¹⁰Po, ²¹⁰Pb and ²²⁶Ra together contribute about 99.75% of the total effective dose through groundwater drinking pathway. All other radionuclides including ²³⁸U contribute only about 0.25% of the total dose. This indicates the necessity of monitoring of these short-lived progeny radionuclides also, apart from their long-lived parents, in the groundwater in the vicinity of uranium tailings ponds during their institutional control period.