This paper presents a trend model of the competitive formation of multi-type inclusions during the cooling and solidification of steel. The model is able to predict the evolution of various inclusions, including their type, composition and size distribution. In the calculations, the thermodynamic library, ChemApp, was applied to perform a thermodynamic equilibrium calculation. Homogeneous nucleation, diffusion-controlled growth and dissolution were employed to simulate the size distribution evolution. At the same time, the collision of inclusions of the same type were considered in a simplified way. The inclusion stabilities were validated by laboratory experiments, which offered a strong basis for the simulations. Using the proposed model, the influence of alloying temperature and oxygen content on the formation of multi-type inclusions was investigated. The results indicated that decreasing the alloying temperature resulted in a higher number density and finer size of different oxides. The oxygen content affected the formation of various oxides in different ways. The predictions, based on the mechanism of competitive nucleation and growth, are discussed and explained. It is believed that the calculations deepen the understanding of the competitive formation of multi-type inclusions. The predicted trends provide a valuable reference for inclusion control and experiment design.Calculation for the Steel Industry (CEQCSI) [10], and classical nucleation and growth theories to model the formation of TiN during solidification. Then, the model was extended to one complex solution for oxides by Lehmann et al. [11], which enabled the calculation of composition changes and size evolution. You et al. [12] proposed a model of MnS formation by combining the thermodynamic library, ChemApp [13], and precipitation kinetics in cases where the collision was considered in a simplified manner. It was found that the aforementioned models were mainly for single inclusion formation, while predictions of the evolution of multi-type inclusions were needed in the development of alloy steels.Based on previous work [12,[14][15][16], the present paper proposes a comprehensive trend model of multi-type inclusions that considers competitive formation during cooling and solidification. This trend model aims at predicting the tendency of particle size and number density, but not the exact values. The model conjoins thermodynamics, kinetics and microsegregation. The thermodynamic library, ChemApp 6.3.4, was applied to perform a thermodynamic equilibrium calculation. Homogeneous nucleation and diffusion-controlled growth and dissolution were employed to simulate the size distribution evolution. At the same time, the collision of inclusions of the same type was considered in a simplified way. Note that the heterogeneous formation of different inclusion types and inclusion clusters and positions are beyond the capacity of the present model. The formation thermodynamics were validated to some extent by laboratory experiments. Using the present model...