We have incorporated the translational rotational (TR) coupling effects in the framework of three body force shell model (TSM) to develop an extended TSM (ETSM). This ETSM has been applied to reveal the second order elastic constants (C11, C12 and C44) in the dilute regimes 0≤ x ≤ 0.47 as a function of temperature for 10K≤T≤300K. The anomalous elastic behavior in C44 below 100 K has been depicted well by ETSM results in the orientationally disordered (ND4I)x(KI)1-x mixed crystals. In order to present a visual comparison of the TRcoupling effect on second order elastic constants, we have evaluated the SOECs with and without TR coupling term in ETSM. Besides third order elastic constants have also been studied and discussed for concentration range 0≤x≤0.47 as a function of temperature for 10K≤T≤300K.