The ideal-MHD stability of a class of tokamak equilibria is analysed numerically by using a spectral code. This class is characterized by flat current distribution in the plasma core and vanishing current at the edge. Both circular and D-shaped plasmas are considered for varying current width, safety factor on axis, βp and aspect ratio. The introduction of a pressureless and current-free plasma layer at the edge stabilizes the residual kink instabilities caused by the non-vanishing current gradient at the surface. The optimum value of β is found to occur at low values of βp (0.25 to 0.4 times the aspect ratio) and reaches 6% for JET.