Twenty-nine experimental determinations of burnout heat flux were made with water flowing by natural circulation through electrically heated vertical tubes with and without internal twisted tapes and through rectangular cross sections of three aspect ratios. Heated lengths varied from 10 to 33 in., system pressure at the test-section flow exit from 14.7 to 26.3 lb/in.2abs, inlet subcooling from 36 to 170 F, and burnout heat flux from 13,000 to 218,500 Btu/h·ft2. Tests were made with both unrestricted and restricted return flow paths. Three correlations were developed for predicting natural-circulation burnout heat fluxes for such conditions. Two are useful for rapid estimation, but the third involves a more fundamental assessment of the coolant-mass velocity at burnout by a graphical matching of the heat flux which a given flow rate can sustain to the heat flux which will produce that flow rate. For all the data, this approach gave average and maximum deviations of 15% and 38%, respectively. It has been found that use of a slip ratio of unity is adequate for burnout prediction, and the reasons for this are discussed in detail. The small burnout penalty incurred by a substantial restriction of return flow path, experimentally observed, is in accord with the theoretical model.