A general anisotropic medium is characterized by 21 elastic constants. In this study we consider only wave propagation along a plane of symmetry of the medium. The maximum number of independent elastic constants is therefore reduced to 13. Stoneley waves at solid-solid interfaces are only possible for certain ranges of values of the elastic constant and density parameters. Considering certain of these parameters to be variables, regions in which waves are possible are calculated for waves traveling in various directions and for media possessing cubic, orthorhombic, and monoclinic symmetries. The results show that the regions in which waves are possible in anisotropic media are similar in outline to those calculated by Scholte (1947) for isotropic media. For certain values of the elastic constants, large variations of the regions from one direction of wave propagation to another are observed. For specific substances in the three symmetry classes given above, the phase velocities of solid-solid Stoneley waves, liquid-solid Stoneley waves, and Rayleigh waves as a function of direction of wave propagation are calculated.