The Gru¨neisen constant and its first order volume dependence, commonly referred to as the second Gru¨neisen constant, are fundamental to the study of many basic phenomena in solids. Knowledge of these two constants enables one to obtain information on the anharmonicity in a solid and to predict a variety of physical properties such as the coefficient of thermal expansion, the equation of state and thermoelastic properties. In the present paper the second Gru¨neisen constant and the pressure dependence of the coefficient of thermal expansion are calculated forCsCl,CsBrandCsIutilizing a volume dependent modified rigid ion model of lattice dynamics . The model parameters are deduced from the three elastic constants and the long wavelength optical mode frequencies. Using the first and second order pressure dependences of these physical observables, the individual second mode‐Gru¨neisen parameters are obtained as a function of wave vector. The temperature variation of the second Gru¨neisen constant is then deduced in a quasi‐harmonic approximation. The second Gru¨neisen constant is also calculated from available thermodynamic data and is in reasonable agreement with the present theoretical prediction. Finally, the pressure dependence of the coefficient of thermal expansion is obtained as a function of temperature.