Preliminary analysis for the S-CO2 Brayton power cycle development suggests small size and high operating speed of turbomachinery. The axial thrust due to the pressure differential generated in the turbomachinery is transferred to the bearing through the shaft. Angular contact ceramic bearings used for high speed operations are incapable of withstanding high axial loads. The current paper presents, theoretical and computational analysis of a 4-hole aerostatic thrust bearing for S-CO2 turbomachinery applications. CFD analysis is performed for different axial clearance gap between stationary and rotating discs of the thrust bearing. The computations have been performed for two different fluids — air and CO2. This computational domain of the flow regime splits into two regions: adiabatic flow through the orifice and isothermal flow in the clearance volume comprising the clearance gap. The influence of the following parameters such as, pressure distribution across thrust pad area, mass flow rate, load capacity and the local velocity in the gap on the stiffness of the bearing are investigated.