The phase diagrams of binary alloys are known to vary with pressure. Within the framework of solution type models, the variation is controlled by the pressure dependence of the elemental members which is relatively well known and that of the interaction parameter which is unknown. We have developed a thermodynamic model linking the pressure dependence of the interaction parameter to the composition dependence of the density and sound velocity. The effect of composition on the sound velocity and density was studied for several binary alloys (such as Bi-Sb ,Bi-Sn and Pb-Sn) and the pressure dependence of the interaction parameter in the solid and liquid phases was estimated. On this basis the pressure dependence of the binary alloy phase diagrams was calculated and found to agree well with the available data.