The structural design of vacuum vessels containing a plasma requires a knowledge of the eddy currents induced by the pulsed magnetic fields employed in these vessels. Consideration of the eddy currents is also indispensable for design of a feedback control system for the plasma position. A method is presented for analyzing the transient behavior of the eddy currents induced in a vacuum vessel consisting of several shell sections each of which is composed of thick plates and bellows made up with thin sheets. This method is based on integro-differential equations with magnetic vector and electrostatic scalar potentials. The charges accumulating at each bellows edge play an important role, and create axially non-symmetric components of the eddy currents. © 1979 The Japan Society of Applied Physics.