An electrical machine for a high-speed flywheel for energy storage in large hybrid electric vehicles is described. Design choices for the machine are motivated: it is a radial-flux external-rotor permanent-magnet synchronous machine without slots in the stator iron and with a shielding cylinder. An analytical model of the machine is briefly introduced whereafter optimization of the machine is discussed. Three optimization criteria were chosen: (1) torque; (2) total stator losses and (3) induced eddy current loss on the rotor. The influence of the following optimization variables on these criteria is investigated: (1) permanent-magnet array; (2) winding distribution and (3) machine geometry. The paper shows that an analytical model of the machine is very useful in optimization.