A numerical study of ideal MHD modes, including both internal and external modes, has been carried out for non-circular tokamaks similar to the JET device. By concentrating on a particular device, a methodology is developed for optimizing achievable beta in a tokamak experiment within the ideal MHD theory. The stability analysis of internal modes is performed with interchange and ballooning mode criteria. External modes are studied with the global code ERATO, including the effect of an infinitely conducting wall at an arbitrary distance from the plasma. By appropriate choice of current profiles, with flat profiles and a low value of poloidal beta being most favourable, plasma equilibria with β above 8% are found which are stable to all modes. No wall stabilization is required for the kink mode. The axisymmetric mode requires feedback stabilization which could be provided by poloidal field-shaping coils. With a wall, β may be slightly improved. Within strict MHD theory where current profiles are arbitrarily chosen, external modes appear to be more restrictive than internal modes.