During the past few years, the high pressure structural phase transition in Rare Earth Compounds has been studied extensively. These materials are mostly ionic in nature; crystallize in the rock salt structures at ambient pressure. In the rare earth compounds, the electrons hybridized between two states, which have nearly equal energy. These properties have been correlated with existence of unfilled f electron shell of RE ions, which therefore interact strongly with the lattice. In the present book a theoretical model has been used in order to understand the effect of f- electrons on phase transition, elastic, mechanical and lattice dynamical properties. The necessity of the development of present two body ineriionic potential model and various interactions required essentially for a complete account of the cohesion in RE compound have been described.We have also discussed Breathing Shell Model (BSM) theory to calculate complete phonon spectrum, density of states and specific heat of Neptunium Chalcogenides in this book.