Numerical simulation is one of the effective methods to solve the magnetohydrodynamic problems in electromagnetic metallurgical reactor. A mathematical statement about magnetic vector potential and electric potential is developed to describe the three-dimensional magnetic field, induced current field, Joule heating power field, and electromagnetic force field in a tundish with channel type induction heating. The resultant equations are solved numerically, and the predicted magnetic field agrees well with the experimental data from the previous reference. The research results show that the magnetic field, the induced current field, the electromagnetic force field, and the heating power are the strongest in the channels, and these fields are eccentric in the channel. In the channel, the induced current is along the axis of the channel, the magnetic field is along the circumferential direction of the channel, the electromagnetic force is along the radius of the channel, and Joule heat power density on the side facing the other channel is greater than that on the side facing away from the other channel.