An immersion apparatus for making ultrasonic measurements in polymers was constructed. A unique feature of this apparatus is that the specimen is held vertically, and the transducers are rotated in order to produce shear waves in the specimen. This arrangement allows measurements to be made through the melting point of crystalline polymers. Sound‐speed measurements, accurate to ±2%, were made on 25 polymers at room temperature and on five of these polymers as a function of temperature. On 15 of the polymers, both longitudinal and shear sound speeds were measured. The longitudinal wave speeds ranged from 2820 to 1020 m/sec, while shear wave speeds ranged from 1230 to 650 m/sec. Using these sound speeds and measured densities, the elastic constants of these polymers were calculated. For four polymers elastic constants as a function of temperature were calculated.