A new method is presented for computing global axisymmetric instabilities of Tokamak plasmas in a conducting shell. The method uses a free-boundary equilibrium code to find displacment vectors compatible with ideal MHD. It is applied to the computation of vertical instability growth rates of highly-elongated, race-track shaped plasmas. Results obtained for up-down symmetric configurations are compared with ERATO calculations. The effects of plasma-wall distance, plasma pressure and current profile are analyzed. In addition, the gain in stability by asymmetric positioning of a given plasma in a given shell is evaluated.