In steelmaking, the reaction of alloying elements with dissolved oxygen, sulfur and nitrogen involves the formation of non-metallic inclusions. Inclusions are usually detrimental for product properties such as fatigue resistance or surface appearance. Hence, steelmakers strive to minimize the number and size of inclusions or to reduce their harmful effect by modifying their composition or shape. More recently, researchers have determined the positive effect of fine dispersed inclusions as grain refiners or heterogeneous nuclei. However, inclusions affect the properties of steel, and adjusting their size, shape and chemistry is crucial to producing advanced steel grades. The present thesis focuses on the computational solution of inclusion kinetics. The thermodynamic library-ChemApp is applied to connect the solution of kinetics in a FORTRAN source code and the thermodynamic databases in FactSage. Kinetics comprises not only the enrichment of solute elements in the solidification process, but also the nucleation and growth of particles. Ohnaka´s analytical microsegregation equation is solved numerically with local partition coefficients coming from thermodynamic databases. The homogeneous nucleation of particles and their subsequent growth is considered; thus, the simulation of single-phase inclusion formation becomes possible. In the present work, manganese sulfides were selected for experimental validation of the modeling results. By incorporating the core concept of the single-phase inclusion model, the competitive formation and dissolution of multi-phase inclusions during cooling and solidification is also modeled. The influences of cooling rate and initial composition on the evolution of the mass fraction of complex oxides, their size, chemistry and number density were investigated in calculations and experiments. The accordance of the results for single-phase inclusions is excellent and still remarkably significant for multi-phase inclusions. In the future, the model will be used to predict experimental conditions for the reliable adjustment of inclusions in ongoing research projects regarding inclusion metallurgy.