The effects of plasma deformability on the feedback stabilization of axisymmetric modes of tokamak plasmas are studied. It is seen that plasmas with strongly shaped cross-sections have unstable motion different from a rigid shift. Furthermore, the placement of passive conductors is shown to modify the non-rigid components of the eigenfunction in a way that reduces the stabilizing eddy currents in these conductors. Passive feedback results obtained using several equilibria of varying shape and aspect ratio are presented. The eigenfunction is also modified under the effects of active feedback. This deformation is seen to depend strongly on the position of the flux loops that are used to determine the plasma vertical position for the active feedback system. The variations of these non-rigid components of the eigenfunction always serve to reduce the stabilizing effect of the active feedback system by reducing the measurable poloidal flux at the flux loop locations. Active feedback results are presented for the PBX-M tokamak configuration.