Expression for second order, third order elastic constant, pressure derivative and Cauchy discrepancy of CsI crystallizing in CsCl structure are presented with the help of (VTSM) model. It includes the effect of van der Waals interactions and three body interactions in the framework rigid shell model. The short-range overlap repulsion is operative to the second neighbor ions. The theoretical results are compared with experimental one by calculating pressure derivative of second order elastic constant SOEC, third order elastic constant TOEC and Cauchy discrepancy. It is concluded that the VTSM is adequately essential for description of Elastic constants and complete lattice dynamics of Cesium Iodide.
