The scattering amplitude for the scattering of anti-plane shear waves by screw dislocations, and of in-plane shear and acoustic waves by edge dislocations are computed within the framework of elasticity theory. The former case reproduces well-known results obtained on the basis of an electromagnetic analogy. The latter case involves four scattering amplitudes in order to fully take into account mode conversion, and an adequately generalized optical theorem for vector waves is provided. In contrast to what happens for scattering by obstacles, the scattering amplitude increases with wavelength, and, in general, mode conversion in the forward direction does not vanish.