The velocities of ultrasonic shear and compressional waves in tungsten crystals have been measured in several directions and as functions of temperature to 1800°C. Adiabatic crystal elastic stiffnesses have been calculated from these velocities as follows:C11=5.2349×1012−4.5967×108T−5.467×104T2±0.25% dyn·cm−2C44=1.6028×1012−1.0320×108T−2.054×104T2±0.25% dyn·cm−2CN=5.2480×1012−3.5005×108T−3.163×104T2±0.25% dyn·cm−2C12=2.0445×1012−0.3403×108T+3.249×104T2±2.3% dyn·cm−2C′=1.5952×102 −2.1282×108T−4.358×104T2±1.8% dyn·cm−2.Values for the elastic constants of random, polycrystalline tungsten were calculated from these crystal stiffnesses. They agree well with values determined on polycrystalline tungsten as functions of temperature.