A theory of concurrent sorption as an instrument for predicting the conditions for desorption of radionuclides, Sr(II) in particular, from “contaminated solid – water” systems is formulated in this presentation. Typical isotherms of concurrent sorption are presented. Based on the sorption isotherm we analyze the possibility of desorption of traces of Sr(II) and Sr-90 from ion-exchange materials. The role of humic acid (HA) in Sr(II) mass transfer in river water and the possibilities of strontium ion desorption from solids with the help of HA solutions are discussed in detail. We describe finally new competitive sorption techniques based on concurrent sorption of the aimed microelement from the contaminated material to the sorbent placed into a specially made pocketed membrane mini-reactor. The investigation is supported by RFBR, project 18-03-00051, and project of UBRAS 18-3-3-5.