The elastic shear stiffness constants of solids, correlated with other cohesive properties, provide a valuable insight into the nature of atomic binding forces. The deviations between calculated and measured values of isothermal bulk modulus of alkali halides have motivated us to frame a model for calculating the same for rock salt and cesium chloride structure alkali halides. The present approach shall include the effect of many body Coulombian, Born-Mayer type overlap repulsive and van der Waals (vdW) interactions in the framework of rigid shell model (R.S.M.). We hope that our results will show excellent agreement with measured isothermal bulk modulus for all the alkali halides.