We investigate the effect of drift kinetic damping on the Resistive Wall Mode (RWM), due to the mode resonance with magnetic precession drifts and/or bounce motion of bulk plasma thermal particles. A self-consistent toroidal drift kinetic model is developed and incorporated into the MHD code MARS-F. The new code (MARS-K) is used to study the RWM stability in ITER steady state scenarios, and to model the Resonant Field Amplification (RFA) for JET plasmas. The self-consistent simulations predict a parameter regime where the RWM in ITER is fully stabilised by the drift kinetic effects combined with the toroidal plasma flow. A wider stable parameter space is predicted by the perturbative approach based on the ideal kink mode eigenfunction. The difference is attributed to the modification of the RWMeigenfunction by the kinetic effects. Applying the MHD-kinetic hybrid code MARS-K to JET plasmas leads to the identification of possible instabilities responsible for the observed RFA at lower beta.