Self-consistent computations are carried out to study the stability of the resistive wall mode RWM in DIII-D J. L. Luxon, Nucl. Fusion 42 , 614 2002 plasmas with slow plasma rotation, using the hybrid kinetic-magnetohydrodynamic code MARS-K [Y. Q. Liu and et al. , Phys. Plasmas 15 , 112503 (2008)]. Based on kinetic resonances between the mode and the thermal particle toroidal precession drifts, the self-consistent modeling predicts less stabilization of the mode compared to perturbative approaches, and with the DIII-D experiments. A simple analytic model is proposed to explain the MARS-K results, which also gives a qualitative interpretation of the recent experimental results observed in JT-60U [S. Takeji and et al. , Nucl. Fusion 42 , 5 (2002)]. Our present analysis does not include the kinetic contribution from hot ions, which may give additional damping on the mode. The effect of particle collision is not included either. Using the CARMA code [R. Albanese and et al. , IEEE Trans. Magn. 44 , 1654 (2008)], a stability and control analysis is performed for the RWM in ITER [R. Aymar and et al. , Plasma Phys. Controlled Fusion 44 , 519 (2002)] steady state advanced plasmas, taking into account the influence of three-dimensional conducting structures.