The invention relates to a package for transporting and / or storing radioactive materials, the lateral body (10) of which has a thickness change zone (14) defining a transition surface (16), and comprising a reduced thickness part (20a) extending from the transition surface (16) towards a first axial end (10a) of the lateral body, this reduced thickness part (20a) comprising an inner surface (24) delimiting laterally a recessed area (26) of the lateral body, also delimited axially by the transition surface (16). In addition, the package includes a side body reconstitution portion (30) extending around the longitudinal axis (2), removably arranged in the recessed area (26), and having an interior surface (34) laterally delimiting a part of the housing cavity (12) intended to receive the set of radioactive materials (13).
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