This paper deals with the electromagnetic field analysis of slotless brushless permanent magnet machines with three different magnetization patterns such as Halbach, parallel and radial magnetization. The magnetization modeling of Halbach, parallel and radial magnetization is performed analytically. And then, analytical solutions for open-circuit field distributions, armature reaction field distributions, flux linkages due to PMs and stator windings, torque, back-emf and inductance are derived in terms of magnetic vector potential and two-dimensional (2-d) polar coordinate systems. The analytical results are validated extensively by finite element (FE) analyses. The magnet volume required in order to produce identical flux density is compared with each magnetization. Finally, analytical solutions and derivation procedures of those presented in this paper can be applied to slotless and slotted brushless permanent magnet AC and DC machines.