The interactions of hydrogen with graphitic C16H10 and B8N8H10 clusters are investigated by performing hybrid density functional electronic structure calculations. The B3LYP results are presented for both the H-C16H10 and H-B8N8H10 clusters. For H-C16H10, significant structural relaxation of the C16H10 substrate is observed, while for H-B8N8H10 the B8N8H10 substrate is allowed to keep a planar structure at their optimized geometry. From the analyses of electron density and potential energy surface, the former interaction is shown to be chemisorption and the latter physisorption. The mechanism of hydrogen adsorption on the substrates is discussed using energetic diagram in the HOMO-LUMO region.