Non-linear reduced MHD modelling of the toroidally rotating plasma response to resonant magnetic perturbations (RMPs) is presented for DIII-D and ITER-like typical parameter and RMP coils. The non-linear cylindrical reduced MHD code was adapted to take into account toroidal rotation and plasma braking mechanisms such as resonant one (~j × B) and the neoclassical toroidal viscosity (NTV) calculated for low collisionality regimes ('1/ν' and 'ν'). Counter toroidal rotation by NTV is predicted for ITER with the proposed RMP coils in 1/ν-limit. Resonant braking is localized near resonant surfaces and is weak compared with NTV in the 1/ν regime for typical DIII-D and ITER parameters. Toroidal rotation leads to the effective screening of RMPs that is larger for stronger rotation and lower resistivity, resulting mainly in central islands screening. Non-resonant helical harmonics (q ≠ m/n) in RMP spectrum are not influenced by plasma rotation, and hence penetrate and are important in NTV mechanism.