The theoretical prediction of surface plasmon frquencies for a supported metal particle system is based on the model as shown in fig. 1. A spherical particle covered with a thin shell of oxide is half embedded in the support. Two surface plasmons (ωH, ωLO) and four surface plasmons (ω1 to ω4) have been predicted by using dielectric theory for the cases of a metal particle sitting on (A) a dielectric insulator and (B) a metal plate, respectively[l-2]. The relative excitation probabilities of those predicted surface plasmons have been calculated using the so-called coherent-state theory[3-4]. Two directions of incidence for the external electron beam are assumed as indicated in fig. 1, P(||) and P(⊥) one is parallel to the Z axis and the other is perpindicular to it. The curves marked with H and L are the calculated excitation probabilities for ωH and WLO as predicted in [1-2]