Abstract: A tube support grid and spacers therefor provide radially inward preloading of heat exchange tubes to minimize stress upon base welds due to differential thermal expansion. The grid comprises a concentric series of rings and spacers with opposing concave sides for conforming to the tubes and V-shaped ends to provide resilient flexibility. The flexibility aids in assembly and in transmitting seismic vibrations from the tubes to a shroud. The tube support grid may be assembled in place to achieve the desired inwardly radial preloading of the heat exchange tubes. Tab and slot assembly further minimizes stresses in the system. The radii of the grid rings may be preselected to effect the desired radially inward preloading.