This study investigates the radiation patterns of an elastic wave field generated by circular plane compressional and shear transducers at the surface of an elastic half‐space. These patterns are obtained from the integral representation of the elastic wave field using the method of steepest descent. It is shown that these patterns contain both effects of the elastic half‐space and the amplitude modulation due to the finite dimension of the transducer source. Examples are given to show the behavior of the radiation patterns at low, medium, and high frequencies. These patterns have been verified by a laboratory experiment performed using circular compressional and shear transducers. Therefore, for a circular transducer (compressional or shear) of a given operating frequency, the transducer radiation directivity can be conveniently analyzed using the results of this study.