System for storing radioactive materials comprising: —a canister (4) containing radioactive waste; —a container (C), provided with a casing (1), a base (2) and a cover (3), and a passive helicoidal convection-based ventilation system provided with: lower air inlets (5); an area (6) of air circulation between the canister (4) and the inner surface of the container (C), and upper air outlets (7); the inlets (5) and outlets (7) have a decreasing variation of section in the direction of air circulation, are curved and facing an oblique direction with respect to the radial direction of the container, the air between said inlets (5) and outlets (7) describing an upward helicoidal path around the capsule or canister (4).