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This paper deals with magnetic field computation of axial flux permanent magnet (AFPM) machines with Halbach and axial magnetized rotor using quasi-3-D analysis modeling. On the basis of magnetic vector potential and polar-coordinate system, the magnetic field solutions due to Halbach and axially magnetized PM rotor are obtained. In particular, 3-D problem, that is, the reduction of magnetic fields near outer and inner radius of the PM is solved by introducing a special function for radial position. The predictions are shown in good agreement with those obtained from 3-D finite element analyses (FEA). Finally, on the basis of derived magnetic field solutions, comparison of AFPM machines with Halbach and axially magnetized rotor is carried out, in terms of magnetic aspects.