Commercial oil-free microturbomachinery implements gas foil bearings (GFBs) for reliable performance with improved efficiency. However, GFB modeling is still largely empirical, lacking experimental validation. An analysis of simple GFBs operating at large shaft speeds (infinite speed number) follows. The bearing ultimate load and stiffness coefficients are derived from simple algebraic equations for the gas film pressures at the equilibrium journal position and due to small amplitude journal motions, respectively. GFBs without a clearance or with assembly interference are easily modeled. The underlying elastic structure (bump foil strip) determines the ultimate load capacity of a GFB as well as its stiffnesses, along with the limiting journal displacement and structural deformation. Thus, an accurate estimation of the actual minimum film thickness is found prior to performing calculations with a complex computational model, even for the case of large loads that result in a journal eccentricity well exceeding the nominal clearance, if applicable. An initial assembly preload (interference between shaft and foil) increases the GFB static stiffness at both null and infinite rotor speeds. At infinite speed, cross-coupled stiffnesses are nil, and thus, GFBs are impervious to hydrodynamic whirl instability.