In this paper, by solving the Maxwell's equations, an analytical model is developed for the prediction of the air gap flux density in the eccentric permanent magnet (PM)-inset machines at no-load and on-load conditions. Since in this model neither Schwartz-Christoffel transformation nor perturbation analysis is used, it is fast and accurate. In the modeling process, the stator of the eccentric machine is replaced with an equivalent surface current (ESC), which is injected at the stator bore. Distribution of the ESC is unknown and must be selected, such that the resultant tangential field satisfies the boundary condition at the stator bore contour. To apply this condition, the flux density of the PMs, armature current, and the ESC are obtained by applying the subdomain analysis and using a conformal transformation. The armature current and ESC are considered as a surface current sheet at the stator bore. The back electromotive force and inductances of the eccentric machine are obtained in the proposed model. In addition, using the Maxwell stress tensor, the unbalanced magnetic force, and the electromagnetic torque are computed. Finally, the model is verified by means of finite element analysis.