This paper presents a general analytical method for predicting the magnetic fields of different Halbach magnet arrays with or without back iron mounted on slotless permanent magnet (PM) linear machines. By using Fourier decomposition, the magnetization components of four typical Halbach magnet arrays are determined. By applying special synthetic boundary conditions on the PM surfaces, the expressions of their magnetic field distributions are derived based on the magnetic scalar potential (MSP), which are simpler than those based on the magnetic vector potential (MVP). The correctness of the method is validated by finite element analysis. The harmonics of airgap flux density waveforms of these Halbach magnet arrays with or without back iron are also compared and optimized.