It is well known that stabilization of the resistive wall mode (RWM) may allow fusion power to be significantly increased for a given magnetic field in advanced tokamak operation. The principle of stabilization of the RWM by rotation has been established both experimentally and theoretically. Recent experimental results have indicated stabilization of the RWM has been achieved with very small levels of rotation using balanced neutral beam injection. The framework of Connor et al. (Connor et al. 1988 Phys. Fluids 31 577) is used to develop two ideal plasma analytic toroidal models where stepped pressure profiles and careful ordering of terms are used to simplify the analysis. The first model has one resonant layer in the plasma and two resistive walls and the second has two resonant layers and one resistive wall.