A product for making, through infusion, a respective drink, in particular a hot drink, especially coffee, the drink being preferably obtained by making the infusion in a respective machine which uses an infusion liquid, which is in particular in the form of water, especially in the form of hot water; the product includes a raw infusion material, preferably in the form of roasted and ground coffee, in a compact configuration, that is, it has the respective constituent particles which adhere to each other. The infusion product extends along an axial direction between opposite longitudinal ends and has a peripheral surface, which is convergent towards a respective longitudinal end in such a way as to engage, and match with, the profile of a corresponding inner surface of a suitable infusion container, in particular in the form of an adapter container.