The liquid steel flow and the particle transport of non-metallic inclusions in the liquid domain inside the strand of a continuous steel casting system are numerically investigated. The whole liquid domain inside the solidified shell is simulated, and the loss of liquid steel due to solidification is considered. Assuming a constant drift velocity, a kind of Euler-Euler multiphase model is implemented to calculate the inclusion behaviour inside the liquid steel, respectively the inclusion removal at the boundaries. The turbulent flow of the liquid steel and the inclusion behaviour are calculated. The resulting distribution of the inclusions in the slab is compared with measurements. The influence of inclusion size (0 to 1 mm) and casting speed on the inclusion distribution is considered.