Of concern are distortionless surface stress waves propagating in a medium which may be nonuniform relative to depth. A similar problem was posed by Burkeetal. [Q. Appl. Math. 183–194 (1976)] where a unidimensional electrical ladder network model, nonuniform along the principle axis, was used in the investigation. Presently, a two‐dimensional development is given based on Hooke’s law and Newton’s law leading to the well‐known Rayleigh‐waves formulation in a uniform medium. It will be seen that broadband high‐pass propagation modes exist along the principle surface. As these propagate along the surface, they are accompanied by a phase change, linear with distance, in the frequency domain, and an associated symmetry change, periodic with distance, in the time domain. Applications may be found in high‐frequency acousto‐optics,insituultrasonic monitoring of elongated bodies, high‐frequency SAW filters, and whenever surface acoustic waves are employed in an environment of high precision or relatively large distances. [Work supported by ONR.]