This paper investigates a two-dimension analytical model for E-core flux-switching permanent magnet brushless machine (FSPMBM) with outer rotor. This method is used to consider the effects of teethes on both the rotor and stator with mathematical method based on integration moreover saturation effect is neglected. This analytical method is implemented for magnetic field calculations in E-core FSPMBM with outer rotor with any combination of rotor-and stator-pole number at no load. To calculate distribution of flux density, initially, the stator and rotor iron is assumed to be infinitely permeable and Maxwell equations are provided then use the boundary conditions at intersection of two sub-regions to find the unknown coefficients for extracting changes of flux density in airgap with respect to each angle and radios. In order to validate the extracted results, the proposed model results are compared with those obtained from finite element method (FEM).