During steel continuous casting non-metallic inclusions and argon gas are brought into the melt pool of the caster. If inclusions become trapped in the solidified strand they can cause undesired defects in the final casting product. Avoiding this particle entrapment into the solidifying shell is important to improve the quality and purity of the continuous cast product. This work focuses on the mold region of a steel continuous caster, including the submerged entry nozzle and the upper part of the solidifying strand. Simulation results of a continuous caster at engineer scale are presented. The turbulent fluid flow dynamics in the steel melt and mushy zone formation, heat transfer and solidification of the steel shell, as well as motion and entrapment of inclusion particles during the casting process are investigated using computational models. The solidification of the strand shell is modeled with an enthalpy-porosity formulation by assuming a columnar morphology in the mushy zone. The predicted thickness of the solidifying shell is validated with experimental data from literature. The trajectories of inclusions and gas bubbles which are continuously injected at the top of the SEN are tracked using a Lagrangian approach. When the inclusions reach the solidification front they can be entrapped/engulfed into the solidifying shell or pushed away from the solidification front, depending on the mushy zone morphology and the forces acting. The entrapment/engulfment of particles into the mushy zone and their final distribution in the solid shell is presented. Parameter studies have shown that the buoyancy of argon bubbles influence the flow field and thus the particle trajectories as well. By considering solidification in the mold, the flow and temperature field is also affected.