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In this work we present a numerical simulation of REELS-spectrum for noble metals,Au and Ag. The calculation is based on an electron-surface inelastic scattering modelpreviously developed. The differential inelastic cross section is obtained fron an inho-mogeneous electron self-energy in the surface region, which provides full informationof the dependency of the total and differential cross section on the kinetic energy,the distance from the surface and the moving direction of electrons, accommodatingthe formulation to the practical situation in surface electron spectroscopes. A novelMonte Carlo simulation code of electron interaction with a surface incorporating thelocal scattering mean free path has been developed. The comparison of the simulatedREELS-spectra with the experimental measurements shows a remarkable agreement onthe spectrum shape, which then confirms that the present model for electron-surfaceinelastic .scattering is quite reasonable. The simulation has further shown the compo.nent to surface excitation due to the individual scattering processes along trajectorypart, i.e., the loss in vacuum before reflection, the loss in vacuum after reflection andloss in metal events.