Rotational stabilization of the resistive wall mode (RWM), with varying E × B flow shear and the radial location of peak shear, is systematically investigated using the MARS-K code (Liu et al 2008 Phys. Plasmas 15 112503), following a non-perturbative magnetohydrodynamic–kinetic hybrid approach. The equilibrium is based on a 9 MA steady state target plasma from the ITER design, except for the plasma flow profile, which is significantly varied in this study. Generally two branches of unstable n = 1 kinetic RWMs are computed (n is the toroidal mode number), depending on the flow amplitude. The first unstable branch, which is normally the more unstable one, is sensitively affected by both the local flow shear as well as the radial location of the peak amplitude of the shear. On the contrary, the second unstable branch, which is often weakly unstable, is less affected by the flow shear. Consequently, stability domains are computationally mapped out in relevant two-dimensional parameter spaces.