The work focuses on modeling of processes occurring in the mold with a new patented cooling system in continuous casting ma chine, in particular, at temperature drop in metal of the stock and in the wall along the height of the mold, on which quality of the resulting billet depends. In the review, works are referred in which slag- forming mixtures (SFM) are investigated that affect heat flow from stock metal to the mold. Foreign authors put emphasis on “soft” cooling of the mold by selection of the SFM. Improvement in process of stock metal cooling in the mold is primarily aimed at improving quality of slab surface, increasing resistance of the mold and increasing productivity of machine, which, according to several authors, can be achieved by mathematical modeling of the process. The problem of mold cooling depends directly on convective motion of liquid steel in the mold, which is considered in a number of works of foreign authors. Use of the principle of heat pipes operation in cooling system of the machine mold, in particular, using porous material with water and air operating medium, as well as the question of liquid droplets evaporation on nanostructured super-hydrophilic surfaces, draws attention of researchers. Cooling of the mold at metal casting speeds of more than 7 m/min, accompanied by an increase in heat flux density, is an urgent task and is considered by a number of authors. Interrelation of the main parameters of the process is determined using Rayleigh dimension theory. Temperature gradient in metal of the mold wall is determined as the main parameter, depending on casting speed (time of stock metal forming in the mold), properties of poured metal (heat capacity, heat conductivity), thermal conductivity of the mold wall, and temperature drop in molded metal. Exponents for similarity criteria are determined taking into account available experimental data on dependence of heat flux density on accepted speed of steel casting, steel parameters. The ratio ∆ t c / t c (where ∆ t c is an average temperature difference across the wall thickness, tc is an average value of a wall temperature) for the mold with the existing and the new (patented) cooling system allows us to determine temperature difference in metal of the billet, which in two compared cooling systems of the mold comprises ∆ t м1 = 450 °С and ∆ t м2 = 231 °С, and the ratio – ∆ t м1 /Δ t м 2 is 1,95 times. Decrease in metal temperature drop ∆ t м2 indicates more “soft” cooling of the mold with a new cooling system.