The problem of long range propagation in a continuously stratified medium is considered for those cases where the stratification is such that a region of slow sound velocity is found to be embedded in a region of relatively faster sound velocity. It is then possible to explain the guiding mechanism of the medium in terms of surface‐wave theory. The technique employed utilizes an equivalent integral‐equation representation for the differential equations describing the boundary‐valve problem, and yields information concerning the dispersive character of the medium. As a means of illustrating the mechanics of this technique and demonstrating its application, dispersion curves are obtained for the particular case of propagation in the sofar sound channel.