The subject of the presented paper is the modeling of strain-stress relationship, which is the main mechanical property characteristic of the behavior of steel subjected to plastic deformation. The major challenge of the research is the temperature of the deformation, which significantly exceeds the hot rolling temperature range. This paper presents the results of work leading to the development of a rheological model describing the phenomena accompanying the deformation of 18G2A grade steel at temperature $1420°C$ and higher. Such temperature is a characteristic of the central parts of steel strands subjected to latest, very high temperature rolling technologies such as integrated rolling and casting processes. Rheological models have crucial influence on the results of the computer simulation of the mentioned processes. The methodology of yield stress curves development requires high accuracy systems of tension and compression test simulation. Hence, the proposed testing procedure is related to dedicated hybrid finite element method system with variable density, which was developed by the authors. The experimental work has been done using the Gleeble® 3800 thermomechanical simulator in the Institute for Ferrous Metallurgy in Gliwice, Poland. The testing machine allows the physical deformation of samples while solidification of their central part is still in progress. The essential goal of the simulation was the computer reconstruction of both temperature changes and strain evolution inside a specimen subjected to simultaneous deformation and solidification. In order to verify the predictive ability of the developed rheological model, a number of compression tests using Gleeble® 3800 simulator have been done, as well. The comparison between the numerical and the experimental results is also a part of the presented paper.

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