Brines with concentrations 3 to 6 or more times the concentration of present sea water occur in subsurface formations. A mechanism is suggested whereby such concentrations can develop, if given time of such magnitude as recognized in geology. Recent work has shown that clay membranes may restrict the transfer of ions in ion-containing water transmitted through them. Under artesian conditions common in geologic basins, water enters aquifers near the outcrop area and is discharged slowly through confining layers in areas where the hydraulic head in the aquifer exceeds the head in the adjoining beds. If either fresh water containing small quantities of ions or formation water containing higher concentrations of ions is transmitted through an argillaceous layer, the transfer of dissolved ions is impeded. The ions that fail to pass the clay membranes thus become concentrated in the aquifer. The mathematical model presented here predicts the distribution of ions within a particular formation under ideal conditions. Although the model is idealized, the theoretical concentrations show a striking similarity to observed concentrations, indicating that this mechanism could explain some of the highly concentrated subsurface brines.