A Green's function method is developed to evaluate the currents induced during startup in the vacuum vessel of ETE (Experimento Tokamak Esférico). The non-homogeneous integral equation for the axisymmetric eddy currents distribution is determined using a thin shell approximation for the vacuum vessel and local curvilinear coordinates. This problem is reduced to a circuit model by adopting spectral representations both for the centreline of the vacuum vessel and the surface current density. Results of this model are compared with the distribution of eddy currents measured in ETE.