Purpose: The article concerns the possibility to optimize the parameters of forging process with the method of thermo-mechanical treatment of steel with microadditions of Ti and V and Ti, Nb and V by means of mathematical modelling of yield stress obtained from conducted plastometric hot compression tests. Design/methodology/approach: To describe the yield stress, rheological model proposed by C.M. Sellars was used. Based on this model, the course of experimental and theoretical stressstrain curves has been verified using a minimum of goal function, for the most accurate matching of analyzed curves of investigated steels. Numerical calculations with the method of finite element method (FEM) were performed taking into consideration test results of compression of specimens in Gleeble 3800 simulator, in a temperature range of 900-1100°C and at the strain rate of 1-50 s-1. Findings: Rheological model assumed in the study, proposed by C.M. Sellars, describing the yield stress of investigated steels with microadditions as a function of strain, strain rate and temperature, proved to be the proper and effective tool for appropriate adjustment of the course of experimental and theoretical a-s flow curves, determined in plastometric hot compression tests. The best matching accuracy of analyzed curves was determined in the work by minimum value of the goal function, which represented simultaneously the best performance of applied inverse solution of finite element method. It has been found that the best matching accuracy of analyzed a-s curves was obtained for constructional steel containing 0.28% C and microadditions of Nb, Ti and V. Practical implications: Optymalization of yield stress values on the new-developed microalloyed steels by the use of mathematical modelling. Originality/value: Obtained results allow to conclude that assumed rheological model along with coefficients, determined with the method of inverse analysis, describe satisfactorily the values of yield stress steels of studied steels.