<p>A thorough understanding of the contact behavior of graded materials is urgently needed for surface design, optimization and reliability analysis in applications such as brake discs, cylinder linings, biomedical implants, flexible electronics, and so on. However, existing models fail to accurately characterize the fretting contact behavior of finite-thickness graded media under complex loading conditions, which greatly hinders various practical and potential applications of graded materials. In this work, a novel generalized model is proposed to analyze the partial slip contact behavior of finite-thickness graded media under both normal and tangential loads. It is found that the proposed model functions well to predict contact tractions, in-plane stress along the graded medium’s surface, as well as the size of stick region. What is more, the anti-fretting performance of graded media can be effectively improved by choosing proper geometric and material parameters. The findings should be helpful not only for the anti-wear design and durability analysis of graded materials in engineering practice but also for the development of contact mechanics.</p>