The generation of nonmetallic inclusions due to mold flux entrapment is detrimental for the final steel quality in the uphill teeming process. Herein, physical and mathematical modeling using a full‐scale mold is conducted to investigate the change of the hump height and the surface height at the free surface during filling. Moreover, the Weber number is also studied to analyze the tendency of mold flux entrapment at the free surface. The results show that the Reynolds stress model can predict the hump height more accurately compared with the k − ε‐based turbulence models. In addition, the result shows that a lower filling rate can result in a lower hump height as well as less fluctuations of the hump and surface heights. Furthermore, the Weber number for the low flow rate case is lower than 12.3, which indicates a small or no risk for mold flux entrapment. The present findings suggest that a reduction in velocity in the mold entrance region are an effective means of reducing the risk of mold flux entrapment.