Four constitutional isomers of diindium dihydride have been studied utilising rigorous quantum mechanical methods. Geometries were optimised with the CCSD(T) method using the aug-cc-pwCVTZ basis set and a small-core pseudopotential for the indium atoms. Relative energetics were determined at the CCSD(T)/CBS level of theory, and the higher order δT(Q) contributions are also computed. The monobridged and vinylidene-like isomers lie 10.8 and 13.6 kcal mol−1 above the planar dibridged isomer, respectively. At 0 K, the trans isomer is the least favoured energetically, differing from the dibridged isomer by 16.6 kcal mol−1. Anharmonic vibrational frequencies were predicted to provide theoretical insight into future experimental studies. Very detailed comparisons are made to matrix isolation experiments from the group of Downs and the group of Andrews. Numerous agreements and disagreements were found.