Problems. In the process of obtaining a strip in a casting and rolling device, the question arises of combining the process of hot rolling of the solidified material and the process of crystallization of the liquid melt. This makes it possible to implement an efficient technology for producing thin-sheet products.
 Purpose of the study. Determination of rational parameters for performing mathematical modeling of material behavior during roll casting requires clearly defined recommendations. The material for the rolling process is steel. The starting material was used in solid, solid-liquid and liquid states.
 Implementation technique. The analysis of the properties of steel was carried out on the basis of the results of experiments obtained at the Physico-Technological Institute of Metals and Alloys of the National Academy of Sciences of Ukraine. To analyze the rheological properties of steel, the dependences of the yield stress for alloyed and carbon steels were used in a certain temperature range. The selected temperature range includes solidus and solid-liquid state of steel, located above 0.8 melting point.
 Research results. Based on the research results, the analysis of the rheological properties of steel in solid, solid-liquid and liquid states during continuous casting-rolling on rolls was carried out. The use of the obtained dependencies makes it possible to perform mathematical modeling of the deformation and hydrodynamics of the material during continuous casting-rolling of steel strips using roll casting-rolling devices.
 Conclusions. The constructed dependences, together with studies of the viscosity of steel in the liquid state and the resistance of steel to deformation in the solid state, most fully describe the rheological properties of steels during casting-deformation processes. The obtained dependences will make it possible to implement an ultra-efficient technology for producing thin-sheet rolled products.