The paper deals with a subdomain model for predicting the magnetic field distribution in surface-inset permanent-magnet (PM) motors with semi-closed slots under load conditions. Due to the presence of electrical current in the stator slots, a magnetic vector potential formulation is used. The magnetic vector potential distribution in each subdomain (air-gap, stator slots, and rotor slots with inset PMs) is obtained by solving two-dimensional Laplace's and Poisson's equations by the separation of variables method. One of the main contributions of the paper concerns the magnetic vector potential expression in the PM region. Indeed, PMs are inset into the rotor iron which leads to solve Laplace's equation with nonhomogeneous Neumann boundary conditions. Magnetic field distribution and electromagnetic torque computed with the proposed analytical method are verified with those obtained from finite-element analyses.