A transient, three-dimensional mathematical model has been developed to study the slag entrapment in a continuous casting mold. The unsteady turbulent flow is computed using the large eddy simulation (LES). The sub-grid scale structure is modeled by the Smagorinsky-Lilly model. The movements of discrete bubbles, as well as three continuous phases (air-slag-steel), are described by solving the coupled discrete particle model and volume of fraction (DPM+VOF) approach. The bubble transport inside different phases (steel and slag) and the escape near the air-slag interface are well studied. Good agreement is obtained by comparing with the plant observation of the slag eyes on the top surface of the mold. Three main mechanisms of slag entrapment are identified; vortex formation, shear-layer instability, and meniscus fluctuation. Four stages are observed for a slag entrapment: deformation, necking, breaking, and dragging in the mold. The model is helpful for understanding the formation of slag entrapment during continuous casting.