The shell stabilization of the tilting mode in a moving ring reactor due to the arrangement of a conductor close to the plasma is studied by numerically calculating the stabilizing torque by the eddy current induced on the conductor surface. The tilting mode instability can be successfully suppressed in the slender ring plasma with the aspect ratio of four by either an internal rod conductor or an external annular conductor. The arrangement of both rod-and annular-type conductors is required for stabilizing the tilting mode in a ring plasma with the aspect ratio of three. The effect of the mutual interaction among the eddy current is shown to be so small as to be safely neglected in calculating the eddy current induced by the tilted plasma, and the simplified treatment of the eddy current is suggested for the computation of the stabilizing torque due to the shell effect.