Sorption of long-lived fission products Cs(I) and Sr(II) by smectite-rich natural clay, originated from western part of India, has been studied by batch sorption method under varying experimental conditions of pH, ionic strength, metal ion concentration and temperature. Low metal ion concentration of Sr in the experiment was achieved using carrier free Sr-85 radiotracer prepared using Rb-85(p, n) Sr-85 nuclear reaction. Ion-exchange-based modelling of sorption data was carried out to delineate the sorption mechanism of fission products. The clay is under evaluation as an engineered barrier and buffer material for Indian deep-underground geo-repository for disposal of vitrified high-level liquid waste. In modelling of Cs(I) sorption data, two sorption sites were found. One of these sites is selective for Cs(I) with high log K value (7.2 +/- 0.2). The affinity pattern for the other site is in conformity with the effect of electrostatic charge of the metal ion in an ion exchange process. Ion exchange in Sr(II) sorption was observed at a single surface site. Affinity of Sr(II) binding to this site (log K = 2.7 +/- 0.1) was found to be higher than that observed for Cs(I) (log K = 1.2 +/- 0.2). To thermodynamically characterize the sorption sites, sorption of Cs(I) and Sr(II) on clay was carried out over 25-55.5 degrees C. Significantly different ratio of thermodynamic parameters (enthalpy and entropy values) was obtained for the two sorption sites of Cs(I) while there was negligible temperature effect for Sr(II) exchange at clay.