The 5 elastic constants of hexagonal cobalt have been determined using pulse modulated ultrasonic waves which are reflected back and forth within the crystal. Frequencies between 10 and 30 Mc/sec were used. Values of the constants were derived from 11 measurements of wave velocities for longitudinal and shear modes in 3 crystals, using a phase comparison technique. At 25°C the constants (all in 1012dynes/cm2) are:c11=3.071±0.5 percent,c12=1.650±0.5 percent,c13=1.027±1.5 percent,c33=3.581±0.5 percent,c44=0.755±0.5 percent. These are based on a density of 8.836.