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Cet in Solidifying Roll - Thermal Gradient Field Analysis As the first step of simulation, a temperature field for solidifying cast steel and cast iron roll was created. The convection in the liquid is not comprised since in the first approximation, the convection does not influence the analyzed occurrence of the [C -> E] (columnar to equiaxed grains) transition (CET) in the roll. The obtained temperature field allows to study the dynamics of its behaviour observed in the middle of the mould thickness. This midpoint of the mould thickness was treated as an operating point for the [C -> E] transition. A full accumulation of the heat in the mould was postulated for the [C -> E] transition. Thus, a plateau at the [T(t)] curve was observed at the midpoint. The range of the plateau existence [t[C] [Lef-right arrow] t[E]] corresponded to the real period of transition, that occurs in the solidifying roll. At the second step of simulation, the thermal gradients field was studied. Three ranges were distinguished: a/ for the formation of the columnar structure (the C - zone): The columnar structure formation was significantly slowed down during incubation period. It resulted from a competition between columnar growth and equiaxed growth expected at that period of time. The relationship was postulated to correspond well with the critical thermal gradient, [G[crit.]]. A simulation was performed for the cast steel and cast iron rolls solidifying as if in industrial condition. Since the incubation divides the roll into two zones (columnar and equiaxed) some experiments dealing with solidification were made on semi-industrial scale. A macrosegregation equation for both mentioned zones was formulated. It was based on a recent equation for redistribution after back-diffusion. The role of the back-diffusion parameter was emphasized as a factor responsible for the redistribution in columnar structure and equiaxed structure.