A containment enclosure for shielding an outer cask containing an inner canister loaded with nuclear waste such as spent fuel rods. The enclosure includes a lower base portion at least partially embedded in a concrete pad and an upper radiation shielding portion defined by a shield jacket coupled to and supported by the lower base portion at a circumferential joint. Cavities of the base and shielding portions collectively define a contiguous containment space for the cask. A portion of the cask resides in each of the base and shielding portions which completely enclose and shield the cask to minimize radiation dosage of personnel in the environment surrounding the cask. The cask is cooled by a natural convectively-driven ambient cooling air ventilation system including air inlets at the circumferential joint of the enclosure. The concrete pad may be part of a spent nuclear fuel storage installation comprising plural cask containment enclosures.