Elastic constants of thermoplastic resin discs are determined by the ultrasonic velocity measurement for the dilatational wave and that for the shear wave and the density. Both of the ultrasonic velocities are obtained with a single system by the immersion sing-around method, changing the incidence angle from water to the specimen. If the incidence angle is below the critical angle, both the dilatational wave and the shear wave propagate in the material. However, if the incidence angle becomes above the critical angle for the dilatational wave in the specimen, only the shear wave propagates in it. Using this phenomenon, both the ultrasonic velocity for the dilatational wave in the specimen and that for the shear wave in it can be obtained independently. From the experimental data the Young's modulus, rigidity, Poisson's ratio and bulk modulus are derived for PMMA, PS and PVC.