Magnetic fields and magnetic forces from magnetic bearings made of circular Halbach permanent-magnet arrays are computed and analyzed. The magnetic fields are calculated using superposition of fields due to patches of magnetization charge at surfaces where the magnetization is discontinuous. The magnetic force from the magnetic bearing is computed using superposition of forces on each patch of magnetization charge. The magnetic force from a Halbach array magnetic bearing is compared to an annular ring bearing of the same dimensions. A comparison is also made between the results obtained using the magnetic surface charge method and the simpler approximate method using a 2-D analytic representation of the Halbach array fields.