The hydrogen adsorption on Al(111) and Ag(111) surfaces have been studied by the charge self-consistent EHT method. It is shown that the H2 molecule would dissociated on Al(111) surface, the H atom could be adsorbed at certain sites with symmetric geometry (such as the threefold, eclipsed, bridge and the atop sites), and H could penetrate into the surface layer and become an interstitial atom. However it is shown that the H2 molecule can be adsorbed on Ag(111) surface with H-H bond paralled to the surface, this result seems to be in fairly good agreement with the result of high resolution electron-energy-loss spectra for H2 on Ag at low temperature. In addition, when the temperature is high, the dissociative adsorption of H2 on Ag(111) surface is also possible.The merit of the method used is discussed.