The sound velocities, bulk modulus, and their pressure and temperature derivatives have been measured on a polycrystalline ZnO by means of a pulse‐superposition method. The pressure derivatives found from the experiments up to 3 kbar at 25°C are: (dv1/dP)=3.643×10−3km/sec·kbar, (dvt/dP)=−3.193×10−3km/sec·kbar, and (dBs/dP)=4.78. The negative value of (dvt/dP) for ZnO is anomalous for crystalline solids. No anomalous behavior was observed in the temperature derivatives near 25°C. They are (dv1/dT)=−1.871×10−4km/sec·deg, (dvt/dT)=−0.392×10−4km/sec·deg, and (dBs/dT)=−0.129 kbar/deg. The Gru¨neisen constant was calculated from the present pressure derivatives of elastic constants and was found to be negative, whereas the value calculated from the thermal‐expansion data at 25°C is positive. This result seems to indicate that the thermal expansivity of ZnO may be negative at very low temperatures.