Abstract On the basis of results of laboratory rolling of flat samples with graduated thickness and measurement of roll forces, values of mean equivalent stress of a Nb-Ti-microalloyed steel were calculated and mathematical models developed in relation to temperature (770 to 1150 °C), strain (ca 0.1 to 0.6, also with including influence of dynamic softening) and strain rate (ca 10 to 150 s-1). An advantage of the given experiment is that by rolling of one sample 4 values of deformation resistance, corresponding to various reductions at the same temperature, can be reached. Another of benefits of this method is uncomplicated mathematical processing of results, namely just thanks to working with values of mean equivalent stress which are less sensitive to various influences than actual values of equivalent stress. The models should be as simple as possible to be used for a fast prediction of power/force parameters in control systems of rolling mills. A single model for mean equivalent stress was not possible to be obtained. Therefore a high temperature model (for temperatures above ca 900 °C) and a low temperature model (for temperatures below ca 850 °C) had to be developed. It was possible to eliminate strain as independent variable for temperatures above 900 °C. These models describe the given relationships with sufficient accuracy, without regard to the type or complexity of the applied equation. Accuracy of the more complex low-temperature model and the simplified high-temperature model is fully comparable.