A unified contact overlap, termed the Minkowski overlap, between any two shapes is proposed in this article. This overlap is based on the concept of the Minkowski difference of two shapes, and particularly on the equivalence between the contact state of the two shapes and the location of the origin relative to their Minkowski difference. The Minkowski contact features of a contact, including the overlap, normal direction, and contact points, are also defined for convex shapes. In particular, an important property of the Minkowski overlap is introduced which lays the solid theoretical foundation for proposing a Minkowski overlap based energy-conserving contact model in the current work.The energy-conserving property for cases where the contact normal direction and point may be subject to discrete changes is also rigorously proved. For 6476