An extended three body force shell model (ETSM), which incorporates the effects of translationalrotational (TR) coupling, three body interactions (TBI) and anharmonicity, has been applied to investigate the temperature dependence of the second order elastic constants (c ij , i, j = 1, 2) of CsCN. The elastic constant c 44 obtained by us shows an anomalous behaviour with the variation of temperature. The variations of elastic constants (c 11 , c 12 , c 44 ) with temperature are almost in excellent agreement with Brillouin scattering measured data. We have also evaluated the temperature variations of the third order elastic constants (c ijk ) and the pressure derivatives of the c ij in the CsCN material. However, their values could not be compared due to lack of experimental data.