This paper deals with characteristic analysis of axial flux permanent magnet (AFPM) machines with axially magnetized PM rotor using quasi-3-D analysis modeling. On the basis of magnetic vector potential and a two-dimensional (2-D) polar-coordinate system, the magnetic field solutions due to various PM rotors 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. And then, the analytical solutions for back-emf and torque are also derived from magnetic field solutions. The predictions are shown in good agreement with those obtained from 3-D finite element analyses (FEA). Finally, it can be judged that analytical solutions for electromagnetic quantities presented in this paper are very useful for the AFPM machines in terms of following items : initial design, sensitivity analysis with design parameters, and estimation of control parameters.