The article presents the results of a mathematical model development for the process of gold leaching from gold-containing ores and concentrates. A mathematical model has been developed by analyzing the chemistry of reactions and mass transfer processes. On the base of a kinetic extraction model and a hydrodynamic complete mixing model a mathematical model of thiosulfate leaching process in various types batch reactors, complete mixing flow process vessels and complete mixing reactor columns with different numbers of vessels in a column has been developed. The effect of the number of reactors in a column has been investigated and optimal segmentation conditions have been found. Based on the investigation of the process using the mathematical model a control system structure has been designed to provide maximum conversion at the exit area of a reactor column.