Aerostatic bearings are the critical parts of ultra-high speed spindles applied to precision milling, grinding, and other precision engineering applications. In this paper, the computational design and analysis of aerostatic journal bearings at ultra-high speed spindles are investigated particularly in light of the nonlinear compressible Reynolds equation and the associated computational analysis and algorithms using the finite element method-based Galerkin weighted residual method. The steady-state static and dynamic behaviors of aerostatic journal bearings are systematically studied, including pressure distributions, load capacity, stiffness, attitude angle, and volume flow rate under conditions of various operating speeds and eccentricity ratios. The coupling of the aerostatic and aerodynamic effects within ultra-high speed aerostatic journal bearings is further explored. The obtained results are formulated as design guidelines for aerostatic journal bearings applied to air-bearing spindles operating in high precision and ultra-high rotational speeds.