A nuclear reactor comprising: a reactor pressure vessel; a cylindrical core barrel supported within and spaced from an interior of the reactor pressure vessel and having a central axis substantially coaxially aligned with a central axis of the pressure vessel; a nuclear core comprising a plurality of fuel assemblies forming a fuel assembly array is supported between a lower core plate and an upper core plate, within and spaced from the core barrel; a shroud (44, 46) is supported between the core barrel and the fuel assembly array, having in part an outer contour that substantially matches an inner contour of the core barrel and an inner contour that substantially matches an outer contour of the fuel assembly array and a hollow interior portion; a neutron reflector positioned within the hollow interior portion of the shroud comprising a closely packed array of elongated rods with an elongated dimension extending in the axial direction; and wherein the shroud comprises horizontal former plates which extend from an inner surface of the core barrel at a plurality of spaced elevations and baffle plates which extend axially between the former plates and substantially form the inner contour of the shroud, wherein the elongated rods of the neutron reflector extend axially between the former plates and in between the baffle plates and the core barrel, wherein the former plates comprise an upper former plate and a lower former plate and characterized in that the former plates constitute a tandem array, and wherein in the tandem array the number of the former plates at the intermediate elevations located between the upper former plate and the lower former plate comprise two former plates stacked back to back. a reactor pressure vessel; a cylindrical core barrel supported within and spaced from an interior of the reactor pressure vessel and having a central axis substantially coaxially aligned with a central axis of the pressure vessel; a nuclear core comprising a plurality of fuel assemblies forming a fuel assembly array is supported between a lower core plate and an upper core plate, within and spaced from the core barrel; a shroud (44, 46) is supported between the core barrel and the fuel assembly array, having in part an outer contour that substantially matches an inner contour of the core barrel and an inner contour that substantially matches an outer contour of the fuel assembly array and a hollow interior portion; a neutron reflector positioned within the hollow interior portion of the shroud comprising a closely packed array of elongated rods with an elongated dimension extending in the axial direction; and wherein the shroud comprises horizontal former plates which extend from an inner surface of the core barrel at a plurality of spaced elevations and baffle plates which extend axially between the former plates and substantially form the inner contour of the shroud, wherein the elongated rods of the neutron reflector extend axially between the former plates and in between the baffle plates and the core barrel, wherein the former plates comprise an upper former plate and a lower former plate and characterized in that the former plates constitute a tandem array, and wherein in the tandem array the number of the former plates at the intermediate elevations located between the upper former plate and the lower former plate comprise two former plates stacked back to back.