The entrapment of inclusions, bubbles, slag, and other particles into solidified steel products is a critically-important quality concern. These particles require expensive inspection, surface grinding and rejection of steel. If undetected, large particles lower the fatigue life, while captured bubbles and inclusion clusters cause slivers, blisters, and other surface defects in rolled products. During continuous casting, particles may enter the mold with the steel flowing through the submerged nozzle. In addition, mold slag may be entrained from the top surface. A computational model has been developed to simulate the transport and entrapment of particles from both of these sources. The model first computes transient turbulent flow in the mold region using Large Eddy Simulation (LES), with the k sub-grid-scale (SGS) model. Next, the transport and capture of over 30,000 particles are simulated using a Lagrangian approach to track the trajectories. A new criterion was developed to model particle pushing and capture by a dendritic interface and was incorporated into the particle transport model. Particles smaller than the primary dendrite arm spacing are entrapped if they enter the boundary layer region and touch the solidifying steel shell. Larger particles are entrapped only if they remain stable while the shell grows around them. The new criterion models this by considering a balance of ten different forces which act on a particle in the boundary layer region, including the bulk hydrodynamic forces (lift, pressure gradient, stress gradient, Basset, and added mass forces), transverse drag force, (caused by fluid flow across the dendrite interface), gravity (buoyancy) force, and the forces acting at the interface (Van der Waals interfacial force, lubrication drag force, and surface energy gradient force). The criterion was validated by reproducing experimental results in different systems. It was then applied to predict the entrapment of slag, particles into the solidification front in molten steel. Finally, the model was incorporated into the 3-D LES model and used to predict the entrapment distributions, removal rates, and fractions of different sized particles in a straight-walled thin slab caster. Although more large particles are removed than small ones, the entrapment rate as defects is still very high.