The principle of correspondence between the; symmetry decompositions of the valence atomic orbitals (AOs) of the central metal and those of the hydride ligands is used to predict and rationalize the geometries of simple transition metal polyhydride complexes, In this orbitally ranked symmetry analysis method (ORSAM) the minimum energy structures have metal AOs whose irreducible representations match those of the hydrides. Tn agreement with previous work, the hydrides prefer to bond to the metal (n + 1)s and nd orbitals, but ORSAM also includes (n + 1)p orbitals in a natural pray and avoids having to postulate hypervalency for transition metal complexes with electron counts greater than 12. Comparison with ab initio structures of 114 simple transition metal polyhydrides shows that: ORSAM correctly predicts and rationalizes the geometries of both classical and nonclassical complexes.