Abstract: The invention relates to a repository (1) for storing radioactive material in a rock formation, wherein there are at least two cavity systems (4, 6) which are spaced apart from each other, and wherein a first cavity system (4) forms a repository chamber (10) for the radioactive material in containers (20) and the second cavity system (6) forms an access system (12), wherein the rock formation is a mountain mass (2), in which the first and second cavity systems (4, 6) are connected to each other via connecting passages (14) at a plurality of transition points, wherein the first cavity system (4) forms a repository chamber (10) in which the containers (20) are free-standing and are accessible and removable, even when the repository chamber (10) is completely full, and the second cavity system (6) forms an access system (12) enabling permanent access and being at a distance from the repository chamber (10) such that the access system (12) forms a radiation-free region for access to the repository chamber (10) at