Measurement of the heat capacity from 2.13° to 10°K and of the elastic constants at 4.2°K have been made on a single crystal of CsI. The Debye temperature at 0°K, &thgr;0, as calculated from the heat capacity is &thgr;0=127.67°K. Values of the elastic constants at 4.2°K arec11=2.725±0.6%,c44=0.873±0.6%, andc12=0.767±3% in units of 1011dyn/cm2. &thgr;0calculated from the elastic constants at 4.2°K is equal to 129.4°K.