A three dimensional numerical analysis method is used to clarify the air-lubrication phenomena of spherical foil bearings in rotary head recording devices. This method is extended for calculating large bearing penetrations encountered under actual operating conditions. Two procedures are proposed for improving poor convergence in numerical calculation. One uses linear extra-polation from solutions for smaller penetrations to obtain initial values close to the solution for larger penetrations. The other stabilizes the calculation by optimizing the relaxation factor between 0.02 and 0.05. This procedure is used to solve problems involving spherical bearing scans with large penetrations on plane and cylindrical foils. The effects of bearing penetration and foil stiffness on the air-lubrication characteristics are presented and discussed.