The current work deals the phenomenon of non-metallic inclusions as a result of the addition of Yttrium as an alloying component. The order of introducing individual components determines its final content in steel. This problem was analyzed using the WYK_Stal program developed at AGH-UST. Individual cases were considered using the accepted thermodynamics models based on Wagner’s formalism. The study of Y2O3 and Y2S3 phase precipitation and the relationship between the addition of Y, Al, Ca, O and S in molten steel was studied using the thermodynamic models. Based on the simulation, the authors stated that, the introduction of aluminum as the final deoxidizer into the liquid steel before the yttrium, results in the formation of non-metallic oxide inclusions. The low oxygen content in the metal bath promotes the formation of yttrium sulphide. In the case of calcium dosing, it is reasonable that, the yttrium is introduced after this element, which limits the losses on the formation of the yttrium sulphide phase.