Herein, a 3D mathematical model is established to elucidate the meniscus solidification and heat transfer in the chamfered mold. The fluid flow, heat transfer, the solidification of steel, the oscillation of the mold, and the steel–slag interfacial tension are considered, and the meniscus behavior on different longitudinal sections and cross sections is discussed. Under the influence of the upper roll flow, the height of the steel level increases from submerged entry nozzle to narrow face, which affects the distribution of the oscillation mark on the surface of the shell. With the mold chamfer and two new corners, the thickness of the slag film at the corner 1 with angle of 123.7° is the largest, and the shell thickness is the smallest, which is related to the 3D profile of the meniscus near the corner. The largest heat flux is located at 10–14 mm below the initial level of liquid steel and is below 3.0 MW m−2. The heat flux at the corner 1 with small obtuse angle is the smallest on the same cross section, indicating that small obtuse angle near the corner resulted in the low heat transfer.