The present work is focused on the pneumatic hammer instability in an aerostatic bearing with shallow recesses and orifices of four different diameters. Operating conditions were zero rotation speed, zero load, and different supply pressures. The diameters of the tested orifices were large compared to the usual practice and correspond to a combined inherent and orifice restriction. The theoretical analysis was based on the computational fluid dynamics (CFD) evaluation of the ratio between the recess and the feeding pressure and on the “bulk flow” calculation of the rotordynamic coefficients of the aerostatic bearing. Calculations showed an increase of the direct stiffness with decreasing the orifice diameter and increasing the supply pressure and, on the other hand, a decrease toward negative values of the direct damping with decreasing the orifice diameter. These negative values of the direct damping coefficient indicate pneumatic hammer instabilities. In parallel, experiments were performed on a floating bearing test rig. Direct stiffness and damping coefficients were identified from multiple frequency excitations applied by a single shaker. Experiments were performed only for the three largest orifices and confirmed the decrease of the direct damping with the orifice diameter and the supply pressure. The identification of the rotordynamic coefficients was not possible for the smallest available orifice because the aerostatic bearing showed self-sustained vibrations for all feeding pressures. These self-sustained vibrations are considered the signature of the pneumatic hammer instability. The paper demonstrates that aerostatic bearings with shallow recesses and free of pneumatic hammer instabilities can be designed by adopting orifice restrictors of large size diameter.