The influence of the superconducting gap anisotropy on the phonon dispersion is discussed for tetragonal and orthorhombic crystals. Superconducting order parameters with different types ofs-wave, as well asd- and (s+d)-wave anisotropies, are studied. We show that along specific directions of the Brillouin zone the lineshape (energy and linewidth) of phonons strongly depends on the anisotropy of the gap. In this context, we discuss recent experimental results performed on YBa2Cu3O7 single crystals. The data can be well described in terms of an anisotropics-wave gap function obtained from the nontotally screened interaction of charge carriers with long-range optical phonons. The calculations suggest, furthermore, that it is generally insufficient to describe experiments that involve the anisotropy of the superconducting order parameter solely in terms of its symmetry. Not only the symmetry, but also the specific structure of the gap as a function of k is important. This conclusion holds for those experiments that are not restricted to the pure determination of the phase of the gap.