### Abstract:

The surface-impedance matrix method is used to study interfacial waves polarized in a plane of symmetry of anisotropic elastic materials. Although the corresponding Stroh polynomial is a quartic, it turns out to be analytically solvable in quite a simple manner. A specific application of the result concerns the calculation of the speed of a Stoneley wave, polarized in the common symmetry plane of two rigidly bonded anisotropic solids. The corresponding algorithm is robust, easy to implement, and gives directly the speed (when the wave exists) for any orientation of the interface plane, normal to the common symmetry plane. Through the examples of the couples (Aluminum)-(Tungsten) and (Carbon/epoxy)-(Douglas pine), some general features of a Stoneley wave speed are verified: the wave does not always exist; it is faster than the slowest Rayleigh wave associated with the separated half-spaces.