The five independent elastic constants of single crystals of hexagonal close‐packed rhenium have been determined by the ultrasonic pulse‐echo technique over the temperature range 4.2°–298°K. The values at 298°K in units of 1011dyn/cm2areC11=61.25,C33=68.27,C44=16.25,C12=27.0, andC13=20.6. The bulk modulus derived from these constants shows a temperature variation somewhat analogous to that which has been reported for other 4d–5dtransition metals. The Debye temperature calculated from the elastic constants at 4.2°K is 416.2°K.