The stellarator Wendelstein 7-X is a steady state fusion experiment being built by the Max-Planck-Institute for Plasma Physics. The magnetic fields which are needed to enclose the plasma are to be supplied by superconducting coils. The steel plasma vessel and a helium cooled heat radiation shield are located between the coil system and the plasma space. Eddy currents are induced in these metal structures during an emergency discharge of the magnet system, The calculation of their effects-force density and heating-is, due to the complex geometry of the system, not possible neither with analytical tools nor by a complete modeling with conventional methods. Therefore, the new modeling method presented here, which is based on the FEM, was developed. In this method the spatial distribution of the magnetic vector potential A(r) is calculated. This calculation is done by a program based on the general Biot-Savart's law Afterwards the calculated vector potential is given, with the help of the method of the Lagrange Multipliers, in time varying form at every node, With the help of these calculations, suitable measures can be taken to reduce the eddy currents and the resulting forces in the cooling shield.