The dissociative adsorption of hydrogen molecule on (100), (110) and (111) surfaces of Ni, Pd and Cu are investigated using the embeded-atom method (EAM). First, the EAM potentials for H-metal surfaces are obtained by fitting the adsorption energies and the length of adsorption bond for single H atom on different surfaces of Ni, Pd and Cu. Then, the activation barriers Ea, adsorption heat q2d and corresponding H-metal bond length R for dissociation of H2 through various pathways are calculated. The potential energy contours for H2 dissociation on (110) surfaces of different metals are presented. The calculated results show that the dissociative adsorption of a hydrogen molecule depend on the species of substrate, the surface orientation and the dissociative pathways. The activation barrier for H2 dissociation on Nisurface is very low, while it is higher for H2 dissociation on Cu surface. The dissociative adsorption of H2 is easier on open (110) surface than that on close-packed(111) surfaces. Among the discussed dissociation pathways, it appears that the most favourable pathway for H2 is that from bridge site to the adjacent centre sites.