Analytical expressions for the ratio of the root mean square fluctuation in atomic positions on the equilibrium lattice positions and the nearest neighbor distance and the mean melting curves of bcc binary alloys have been derived. This melting curve provides information on Lindemann’s melting temperatures of binary alloys with respect to any proportion of constituent elements and on their euctectic points. Numerical results for some bcc binary alloys are found to be in agreement with experiment. Keywords: Lindemann’s melting temperature, eutectic point, bcc binary alloys. .