A simple model of a toroidal, high- β quasi-uniform current model of a tokamak with elliptic cross-section is investigated for stability against uniform vertical displacements. On the basis of asymptotic theory, it is shown that for high- β/toroidal effects to be important β must be of order the equilibrium limit. For a given β and ellipticity the mode can always be stabilized by a conducting wall placed sufficiently close to the plasma. Although the plasma is displaced rigidly the toroidicity leads to both m = 1 and m = 2 harmonics in the perturbed vacuum field.