Equilibrium-dynamic modeling methods have been used to evaluate the possibility of redeposition of the previously formed vein Pb-Zn ore material on the carbonate barrier during the reactivation of the hydrothermal system. The natural prototype is the Ursdon ore occurrence (Dzhimidonskoe ore field, North Ossetia, Russia) localized in Oxfordian limestones (J3), and the formation of polymetallic vein deposits in the area took place in the pre-Callovian time of the Middle Jurassic. The calculations were performed using the HCh software package, which includes the Unitherm thermodynamic database (H-O-K-Na-Ca-Mg-Al-Si-Fe-C-Cl-S-Zn-Pb-Cu system, described by 54 minerals, 78 particles of an aqueous solution). It has been established that late low-temperature hydrothermal solutions can provide pyritization, silicification and the formation of Pb-Zn mineralization in carbonate rocks. The deposition of quartz and sulfides occurs along cracks and at the dissolution front of carbonate rocks.