A nuclear steam supply system utilizing gravity-driven natural circulation for primary coolant flow through a fluidly interconnected reactor vessel and a steam generating vessel. In one embodiment, the steam generating vessel includes a plurality of vertically stacked heat exchangers operable to convert a secondary coolant from a saturated liquid to superheated steam by utilizing heat gained by the primary coolant from a nuclear fuel core in the reactor vessel. The secondary coolant may be working fluid associated with a Rankine power cycle turbine-generator set in some embodiments. The steam generating vessel and reactor vessel may each be comprised of vertically elongated shells, which in one embodiment are arranged in lateral adjacent relationship. In one embodiment, the reactor vessel and steam generating vessel are physically discrete self-supporting structures which may be physically located in the same containment vessel.