In this paper, the sorption behavior of Cs+ and Sr2+ on column of fucoidic sands under dynamic flow conditions was investigated, and their sorption capacities (SC) towards these two cations were studied. The determination of SC is based on the construction of respective breakthrough curves using 137Cs and 85Sr radionuclides as isotopic indicators in laboratory experiments. The samples were taken from several parts of the borehole in the area of interest. Undisturbed cores of 5 cm in diameter and 10 cm long were put in the glass columns and the cores were perfectly tightened using acrylate resin. In this time-dependence study, the so-called cenoman background groundwater was used. A concentration of 10−6 mol/dm3 of Cs+ and Sr2+ in liquid phase individually was established using neutral salts of CsNO3 and Sr(NO3)2, respectively. The groundwater was introduced at the bottom of the columns by a multi-head peristaltic pump, at a constant flow-rate of about 4 cm3/h. The results show that the sorption capacity of the investigated fucoidic sands for 137Cs and 85Sr is 0.1–1.5 and 0.05–0.5 μmol/100 g, respectively, in dependence on the evaluation of corresponding breakthrough curves. Some differences in the behavior of the cores during the experiments have also been observed and explained.