We report the results of our investigation of some stationary points on the singlet and triplet potential energy surfaces of Al2O4, one of the products tentatively identified in the Al + O-2 reaction in cryogenic matrices. The computations are done at the SCF, MP2, B3LYP, and CCSD(T) levels using one-particle basis sets ranging from 6-311G(2d) to 6-311+G(3df). Several geometries are considered, and a structure with D-2h symmetry is found to be the most stable isomer. Electron correlation is important for the quantitative determination of the relative energies of the various isomers. Vibrational frequencies and isotopic frequency ratios are computed for the most stable structure, and a comparison is made with values determined from cryogenic matrix studies. The dissociation energy, D-e, for the process Al2O4 --> 2AlO(2) is estimated to be 183 kcal/mol.