Two approaches for studying the damping of resistive wall modes due to wave particle resonant interactions are discussed. One approach uses the eigenfunction from an ideal MHD code combined with the resonant particle damping calculated from a drift-kinetic δf- method formulation. This perturbative approach treats the wave-particle interaction precisely, but does not include the back-effect of the kinetic terms on the eigenfunction structure. In the alternate non-perturbative approach the kinetic terms are included in an MHD description via the pressure tensor. This non-perturbative approach includes the resonances due to the bounce and precessional drifts subject to certain approximations. Comparisons between the two approaches and conclusions on the dominant stabilizing mechanisms are presented.