Aiming to investigate the behavior of non-metallic inclusions near an advancing solid-liquid interface and the effect of a pulsed magnetic field on the distribution of inclusions, motions of inclusions without and within a pulsed magnetic field were observed in real-time during the solidification of 45 steel. The distribution of inclusions and the evolution of the microstructure were investigated. It was found that a pulsed magnetic field favors the engulfment of inclusions. A uniform distribution of inclusions was obtained. The microstructure was mainly composed of acicular ferrite within the pulsed magnetic field. A mathematical model was proposed to describe the reaction between inclusions and the advancing solid-liquid interface and the phenomenon of inclusion engulfment/pushing by the solidification interface. Furthermore, the critical velocity of inclusions to be engulfed was calculated. It can be concluded that the numerical value of the critical velocity of inclusions to be engulfed differs from the experimental value. After the revision of the mathematical model, the numerical value of the critical velocity was about 4.47 μm/s, validating the experimental value.