The elastic constants of single‐crystal tungsten between 4.2 and 77 K have been measured utilizing a sampled continuous‐wave technique. The sensitivity of the present technique is such that the temperature dependenceCij(T) below 77 K is explicitly observed for the first time. A diffuse anomaly inCL(T), whereCL= 1/2 (C11+C12)+C44, is observed in the temperature range 15–22 K.