The anthropogenic accidents in the world (including the underground emergency nuclear explosion at the site “Kraton-3” (Yakutiya) and also the recent Fukushima accident) resulted in significant environmental pollution by radionuclides, mainly long-lived 90Sr and 137Cs. One of the ways to solve this problem is the creation of “permeable reactive barriers” (PRBs). High selectivity of clinoptilolite-containing tuffs (CLT) towards Sr2+ and Cs+ radionuclides, together with their availability and reasonable cost, make possible their use as PRBs. The scales of the ion-exchange processes taking place on PRBs indicate the necessity of mathematical modelling. In this connection, Sr2+ and Cs+ ion-exchange sorption on Khonguruu CLT (Yakutiya) from solutions of various mineralizations was studied under equilibrium and non-equilibrium conditions. The physicochemical and mathematical models of the dynamic ion-exchange process and also the computer program considering both structural features of CLT (two-stage particle diffusion kinetics) and possible periodic interruptions of the process were developed. The breakthrough time of CLT as a geochemical barrier was calculated by such mathematical modelling.