The paper deals with the low-frequency diffraction of a plane compressional elastic wave incident obliquely on a rigid circular disc embedded in an infinite elastic medium. The motion of the disc, both rotational and translational, has been discussed in detail. By letting the mass of the disc go to infinity one obtains the results for diffraction by a fixed disc. Far-field amplitude of the scattered field has also been obtained. This can be used to calculate the scattering cross-section of the disc. It is found that for long wavelengths the scattering coefficient varies as the fourth power of the wave number if the disc is movable, whereas it is independent of the wave number if the disc is fixed.