High-speed permanent magnet rotors need a non-magnetic enclosure so as to ensure structural integrity of the rotor at elevated speeds. Optimal design of the enclosure is the focus of this paper. Analytical modelling of mechanical stress in the rotor is presented. The model distinguishes between influences of enclosure geometry and fitting on the stress, while also considering rotational speed and operating temperature. Through analytical modelling, a relatively simple approach of optimizing the enclosure is achieved. This optimization approach was used in the design of a carbon fibre enclosure of an unconventional high-speed rotor with a disc shape. It is shown that a planar analytical model of stress with isotropic material assumption is sufficiently good for structural optimization of a permanent magnet rotor.