Bump foil bearings without nominal radial clearance were analyzed. An air film thickness model and a bearing theoretical analytical model were developed accounting for air compressibility and foil deformation. To analyze hydrodynamic characteristics of bump foil beatings with different operating eccentricities, the air film thickness equation and Reynolds equation were coupled through pressure and solved by Newton-Raphson Method(NRM) and Finite Difference Method (FDM). The characteristics of an bump foil bearing model were dis-cussed including load carrying capacity, film thickness and pressure distributions. The results of simulation show that bump foil beating without nominal radial clearance can provide better stability and greater load capaci-ty. This numerical analytical method also reveals a good convergence in numerical calculation.