Abstract Magnetoelastically coupled vibration of the fusion reactor first wall was investigated in light of the magnetic damping effect. A law of similarity for the coupled vibration is proposed by non-dimensionalizing a set of equations describing the coupled problem between the elastic vibration and the eddy current field. The law was verified through numerical experiments. In addition, the dynamic behavior of the ITER first wall during plasma disruption was simulated, taking into account the magnetic damping effect. It was found that the dynamic stress is overestimated by neglecting the magnetic damping. This effect significantly reduces the dynamic stress in the case of a thin first wall, so that the flexible thin shell structure is found to be applicable to fusion reactor components.