The Dissertation is a complete independent research with scientific bases of determination of a specific connection between the secondary salt halos of dispersion of chemical elements and ore objects in the territory of the Ukrainian Shield. It allows to make the most effective local mineral prediction and search prospecting in the territory of the Ukrainian Shield with the least money expenditures. Efficiency of application of different geochemical methods depends on geochemical and landscape conditions, relief and geological structure, characteristic of sedimentary rocks and many other factors. The perfection and development of geochemical prospecting methods recall for elaboration of new methods and methodological approaches. One of such possible and effective approaches is a mathematical simulation of formation conditions of the secondary salt halos of chemical elements dispersion with the purpose to determine their connection with ore objects. Sedimentary mantle of the Ukrainian Shield appears to be the main obstacle for ore deposits discovering. However, it is in the sedimentary deposits which overlap ore manifestations there occurs a formation of the secondary salt halos of chemical elements dispersion that determines a possibility of effective use of geochemical methods in metallic minerals, prospecting. Using of methods of thermodynamics analysis and mathematical simulation the author has calculated the basic forms of chemical elements as indicated forms at prospecting minerals depending on pH of the natural environment. Computation of equilibrium in multicomponent systems is executed by the program PHREEQC (migrations of elements, that allows for all possible forms, and all competing reactions, which take place in the system) with the use of the methods of thermodynamics analysis and mathematical simulation at different temperatures and different pH. Different forms of migration of chemical elements were calculated at three temperature values - 15, 25, 35 °C and different pH - 6, 7, 8 (in different types of soils). It was determined that at a temperature 15-35 °C the content of different forms of chemical elements does not change essentially. That is the temperature has not to be taken into account when determining stability of mobile forms during their migration is; at pH 3 - 6 the prevailing form of migration of all elements is cationic or anionic. Further computations helped to find out that the cationic and anionic forms Cl-, K+, Mn3+, SO42- at any physical and chemical terms of the environment make above 90 % of the mobile forms total of each chemical element. Since the simple cationic and anionic forms of chemical elements have the highest value for the searches, it is expedient to use an ion-selective method for determining cations and anions. Using the methods of mathematical simulation the author has determined conditions of formation of the secondary salt halos and revelation of their anomalies for determining ore exposure prospects. The mathematical simulation was executed with some assumptions because it was difficult to consider and use the all factors of the secondary salt halos formation. A steady-state three-dimensional axi-symmetrical model of mass transfer was developed and realized in heterogeneous environment. It takes into account the processes of diffusion and convection. A number of models that take into consideration ore's or tracer's elements outcrop was created and dependence of formation of the secondary salt halo on the type and power of sedimentary deposits, that overlap ore manifestations is determined. When studying formation of the secondary salt halos above the ores' manifestation at different depths of occurrence the author made a conclusion that the anomalies of mobile forms of chemical elements could be fixed even at the sedimentary layers thickness above the ore body of over 100м, and in some cases more. The author has developed: a scientific basis for determination a specific connection between an integral content of chemical element over the area of the secondary salt halo with its integral content on the area of ore body that allows to determine the diameter of ore body over the parameters of the secondary salt halo and content of ore's element on its surface. The author has proved for the first time the existence of horizontal zoning of the Ukrainian Shield territory using a mobility of chemical elements in the ground deposits. There is the increase of mobility of chemical elements from South to North, that is determined by the increase of soils moistening and change of oxygen-alkali terms. Allowing for the complex factors of terms of formation of the secondary salt halos of chemical elements dispersion, the author had first carried out the zoning of the Ukrainian Shield territory by the terms of formation of the secondary salt halos and by the terms of the use of geochemical prospecting of minerals according to the secondary salt halos of dispersion Keywords: the secondary salt halos, ore formation, mathematical simulation, forms of migration, sedimentary rocks.