Surface inset permanent magnet DC machine can be used as an alternative in automation systems due to their high efficiency and robustness. Magnet segmentation is a common technique in order to mitigate pulsating torque components in permanent magnet machines. An accurate computation of air-gap magnetic field distribution is necessary in order to calculate machine performance. An exact analytical method for magnetic vector potential calculation in surface inset permanent magnet machines considering magnet segmentation has been proposed in this paper. The analytical method is based on the resolution of Laplace and Poisson equations as well as Maxwell equation in polar coordinate by using sub-domain method. One of the main contributions of the paper is to derive an expression for the magnetic vector potential in the segmented PM region by using hyperbolic functions. The developed method is applied on the performance computation of two prototype surface inset magnet segmented motors with open circuit and on load conditions. The results of these models are validated through FEM method.