Radionuclides transport in groundwater system is described using a numerical method in Matlab. The activity concentration and annual committed effective dose (ACED) to the public from consumption of the natural radionuclides 238U and 232Th were determined. The maximum activity concentrations were around 0.3 Bq/L, and 0.08 Bq/L for 238U and 232Th respectively. The activity concentration tends to be neglected at 1500 m for 238U and 1000 m for 232Th. from the discharged point. The corresponding annual committed effective dose estimated was 0.022 mSv/y. The results obtained for this study are far below the recommended levels of 10.0 Bq. L-1 and 1.0 Bq. L-1 for 238U and 232Th respectively for drinking water established by the WHO and 1 mSv per year dose limit recommended by the ICRP for public radiation exposure.