Electrical machines with rare-earth permanent-magnets (PMs) exhibit high torque density and good efficiency over a wide operation range. However, the high cost and limited reserves of the rare-earth material makes it less sustainable to develop this machine technology for electric vehicle (EV) traction. To improve machine performance and reduce PM usage, this thesis investigates a number of issues pertinent to modelling and design of PM machines for EV traction applications. A four-wheel vehicle dynamic model is established to quantify the influence of tyre slip on machine sizing, and thus an optimum control for torque split ratio of distributed front-rear drives is realised by minimising the loss resulting from tyre slip. PM-assisted synchronous reluctance machines with fractional-slot windings are proposed to reduce PM usage whilst exploiting advantages of fractional-slot windings. To more accurately evaluate reluctance torque and thus maximise torque production of an interior PM (IPM) machine in design stage, a torque model allowing for torque component separation via frozen permeability is presented. A generic approach to magneto-motive force harmonics reduction using multiple 3-phase windings is proposed to reduce rotor iron loss and torque ripple whilst improve reluctance torque and machine efficiency. A 9- phase 18-slot 14-pole IPM machine is subsequently designed based on the proposed multiple 3-phase windings and its performance validated on a 10kW prototype. In order to accurately assess the performance of an IPM machine drive, a high-fidelity and computationally efficient machine model is proposed by considering magnetic saturation, spatial harmonics, iron loss and temperature effects. Furthermore, an electro-thermally coupled model is established by integrating the temperature-dependent electromagnetic model with a state-space lumped parameter thermal model. Both models are experimentally validated. An analytical mechanical stress model is proposed to incorporate mechanical strength constraints into machine global optimisation process. Thus, unfeasible designs whose mechanical strength cannot meet the requirement can be avoided.