In this paper, in order to achieve the sinusoidal back electromotive force (EMF) waveform in a permanent-magnet machine, which is closely related to its magnet shape, we have used magnet arc shaping technique. An analytical analysis based on Maxwell equations is proposed for calculating magnetic field and thrust/torque. Then the accuracy of the presented method in modeling of machine is verified by the finite-element method. Finally, a magnet shape design is carried out based on the analytical method to produce sine air-gap magnetic field. The results show an enhancement in optimized motor performance.