Velocity of both longitudinal and transverse ultrasonic waves in polystyrene and polymethyl methacrylate is measured over the temperature range -60° to 90°C. Values of the bulk-modulus, shearing modulus, and Poisson's ratio are computed from the measurements. It is found that each curve of the velocity-temperature and of the moduli-temperature changes its slope at the temperature near the second order transition and that this temperature is independent of frequency. Measurements are also made on polymethyl methacrylate of different moisture contents. Water being absorbed, the shearing modulus becomes smaller but below room temperature the bulk-modulus becomes larger. Comparing with the density-temperature characteristics, this effect of absorbed water is explained as due to the decrease of the free volume and the plasticizer effect caused by the entry of water.