An analysis of the effect on the wall stabilization of external kink modes due to toroidally continuous gaps in the resistive wall is performed. The effects both with and without toroidal rotation are studied. For a high-beta equilibrium, the mode structure is localized on the outboard side. Therefore, outboard gaps greatly increase the growth rate when there is no rotation. For resistive wall stabilization by toroidal rotation, the presence of gaps has the same effect as moving the wall farther away, i.e., destabilizing for the ideal plasma mode, and stabilizing for the resistive wall mode. The region of stability, in terms of wall position, is reduced in size and moved closer to the plasma. However, complete stabilization becomes possible at considerably reduced rotation frequencies. For a high-beta, reverse-shear equilibrium both the resistive wall mode and the ideal plasma mode can be stabilized by close fitting discrete passive plates on the outboard side. The necessary toroidal rotation frequency to stabilize the resistive wall mode using these plates is reduced by a factor of three compared to that for a poloidally continuous and complete wall at the same plasma-wall separation. (C) 1996 American Institute of Physics.