This paper presents a numerical investigation on the effect of hydrostatic pressure (lithostatic stress) and confining pressure (horizontal tectonic stress) on percussive drilling of hard rocks. A finite element based modeling approach was employed in the simulation of the dynamic bit-rock interaction process. The rock fracture in this approach is modeled with a damage-viscoplasticity model accounting for the main fracture types in the bit-rock interaction as well as the strain-rate effects. The model was calibrated for Kuru grey granite in the unconfined case. In the simulations of single impact with a multiple-button bit both hydrostatic and confining pressures were applied at different levels up to 100MPa and the results were compared to the case with no pressure. The simulations show that at this pressure level the volume of the failed elements was 38% in case of hydrostatic pressure and 56% in case of confining pressure of the volume in the pressure free case. The same figures apply to corresponding rates of penetration. The cause of this reduction in the material removal or the rate of penetration is the compressive stress state, of either pressure type tested, which effectively suppresses tensile and shear fractures.