<b>Phonon Modes and Elastic Properties of RE55Al25Co20 Bulk Metallic Glasses</b> The present paper deals with the theoretical study of phonon modes and elastic properties of RE55Al25Co20 RE Rare Earth =Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu bulk metallic glasses. The Hubbard Beeby approach combine with Jani et al. local model potential has been utilized to compute the collective modes for present glasses. Three different local field correlation functions of Hartree H , Taylor T and Farid et al F are employed to find the influence of the screening effects on the collective modes of RE55Al25Co20 bulk metallic glasses. The calculated phonon dispersion curves show all broad features of the collective excitation. It observed that out of three local field correction function, Taylor and Farid et al screening functions give better agreement with experimental values compared to other screening functions. Overall, the present results of elastic properties are found to be good agreement with experimental results. Bulk Metallic Glass, Pseudo potential, Local field correction function, Collective modes, elastic properties 802-807 Issue-6 Volume-4 P. H. Suthar