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.