In this paper, a simplified nonlinear finite element for bump foil forming process of foil air bearings is developed. The bump foil is dealt with as flexible deformable body, the upper die and lower die are considered as the rigid body without deformation. The friction model between bump foil and dies with velocity-dependent friction forces is described by arctan function. The forming process of SS304 Stainless Steel bump foil under different loads is investigated with rigid-plastic finite element method. The simulation results are compared with theoretical values and experimental results. Therefore more feasible process parameters are obtained to fabricate the bump foils.