The non-linear reduced four-field RMHD model in cylindrical geometry was extended to include plasma rotation, neoclassical poloidal viscosity and two fluid diamagnetic effects. Interaction of the static resonant magnetic perturbations (RMPs) with the rotating plasmas in tokamakswas studied. The self-consistent evolution of equilibrium electric field due to RMP penetration is taken into account in the model. It is demonstrated that in the pedestal region with steep pressure gradients, mean flows perpendicular to the magnetic field, which includes E → × B → and electron diamagnetic components plays an essential role in RMP screening by plasma. Generally, the screening effect increases for lower resistivity, stronger rotation and smaller RMP amplitude. Strong screening of central islands was observed limiting RMP penetration to the narrow region near the separatrix. However, at certain plasma parameters and due to the non-linear evolution of the radial electric field produced by RMPs, the E → × B → rotation can be compensated by electron diamagnetic rotation locally. In this case, RMPs can penetrate and form magnetic islands. Typical plasma parameters and RMPs spectra on DIII-D, JET and ITER were used in modelling examples presented in the paper.