A particle-entrapment model based on local force balances has been developed, implemented into computational models of turbulent fluid flow, and applied to simulate the entrapment of slag inclusions and bubbles during the continuous casting of steel slabs. Turbulent flow of molten steel is computed in the nozzle and mold using transient CFD models. Next, the transport and capture of over 30,000 particles are simulated using a Lagrangian approach. Particles touching the dendritic interface may be pushed away, dragged away by the transverse flow, or captured into the solidifying shell according to the results of a local balance of ten different forces. This criterion was validated by reproducing experimental results in two different systems. Finally, the model is applied to predict the entrapment distributions of different sized particles in a typical slab caster. Although more large particles are safely removed than small ones, the capture rate as defects is still high.