According to the invention, anti-matter can be stored in a spherical shell container (10) and is introduced into or extracted from the latter by being loaded in an attached piece (42) adjoining an.opening in the container from the exterior of the sphere into its interior, and this always taking place without touching the container wall and attached piece, which consist of matter. In accordance with a particularly preferred exemplary embodiment; spherical shell segments (18) generate in the interior of the sphere an electrostatic field which keeps electrically charged anti-matter in a stable position in a fashion centered about the center of the sphere of the storage system.