A systematic numerical investigation is carried out to understand the effect of variation of the equilibrium pressure pedestal structure on the H-mode plasma response to the applied resonant magnetic perturbation (RMP) field in tokamaks. The plasma response to the n=1−4 (n is the toroidal mode number) RMP fields is computed and analyzed utilizing the toroidal MHD code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681). The edge safety factor is fixed while varying the pressure pedestal height or width in the single-null (SN) and double-null (DN) divertor-like configurations. The key results are: (i) the optimal coil current phasing for ELM control, between two rows of RMP coils, is independent of the assumed pedestal height or width, (ii) with the same coil current and optimal coil phasing, a higher pedestal height generally leads to less edge-peeling response of the plasma and thus more challenge to control ELMs, and (iii) a wider pressure pedestal generally increases the edge-peeling response and hence favors ELM control. These results hold particularly well for n>1 RMPs, for both the SN and DN plasmas.