Multiple prompt γ-ray analysis (MPGA) and conventional neutron-induced prompt γ-ray analysis (PGA) are nondestructive analytical methods for bulk chemical compositions, and their analytical capabilities were compared for elemental analyses of geological and cosmochemical samples. Detection sensitivities of PGA are often restricted by poor signal-to-noise ratios and interferences from different origins. MPGA can substantially reduce the background level, especially for hydrogenous samples, relative to PGA, which opens up a possibility to use lower energy prompt γ-rays of some trace elements. Although it is one of the major constituent elements of rock samples, Mg is hard to be determined by PGA. With MPGA, Mg contents could be determined with reasonable consistency with their corresponding recommended values in geological and cosmochemical samples by carefully selecting suitable coincident prompt γ-ray energy pairs without interference correction. MPGA was applied to a hydrogenous meteorite, Ivuna, which contains H at 2% mass level. MPGA detection limits for most of the elements studied can be reduced up to 1 order of magnitude when compared with PGA detection limits under the present experimental conditions.