[en] The inclusion of high-ß and first-order toroidal terms in the reduced set of (resistive) MHD equations affords the possibility of improving the study of tokamak plasma behaviour by three-dimensional numerical simulation. A new code, GALA, based on the reduced equations is developed. It is used to analyse the linear and nonlinear behaviour of the internal kink mode in equilibria which are generated by a simple relaxation procedure. We find that the inclusion of toroidal effects in high-ß equilibria provides considerable stabilization. (orig.)