For given geometry of a shrink fit, a further essential design parameter is the interface pressure between inclusion and hub to reliably transfer a moment under all operating conditions in the specific application. Hence, in general a large interface pressure shall be achieved, and this may be facilitated by an elastic–plastic design. Furthermore, minimizing the weight of the device becomes increasingly important in engineering, too. To achieve both objectives, in the present semi-analytical study of a shrink fit with solid inclusion a combined elastic–plastic design and use of a functionally graded hub is proposed. As is shown, by appropriate grading not only the weight of the hub can be reduced noticeably as compared to a homogeneous one but also a much better behavior at rotation can be achieved, and admitting partial plasticization can further improve the performance; as an example, a shrink fit with steel/aluminum FGM-hub is discussed comprehensively.