The simulation of eddy currents induced in the vacuum vessel and central column of spherical tokamaks is discussed, improving upon previously published methods. The present model allows us to describe the vacuum vessel either as a thin shell or as a large collection of rings, formally reducing the problem to a set of coupled circuit equations. Results are compared with measurements of the electromotive force and current distribution on the vacuum vessel of the ETE spherical tokamak. The mathematical model is described in detail, enabling application to other machines.