In the present work an investigation of constitutive equations is made to obtain good fit to experimental data and ensure proper extrapolation out of experimental range of plane strain compression tests to low and high values of Zener–Hollomon parameter, which are required in finite element modelling. A computer program for optimisation of rheological parameters of material was developed. Optimisation using experimental data for two ultra low carbon steels was made and the results are compared with measured stress–strain curves. The obtained constitutive equations were used in the finite element model and comparison between experimental and computed displacement–force curves is made. The influence of inhomogeneity of strain rate, strain and temperatures distribution during compression tests on flow curves is illustrated.