A toroidal, elliptic cross‐section, sharp‐boundary model of a high‐pressure tokamak with currents confined to the surface, is tested for stability against kink modes. It is shown that the optimum configuration corresponds to a vertical ellipse in which the ratio of the major to minor axes is 2.2. For this case, the maximum critical&bgr;for stability against kink modes is&bgr; = 0.37a/R.For&bgr; > 0.37a/Rthe model is unstable for all values of the safety factor above and below the Kruskal‐Shafranov limit.