Abstract
A review of some theoretical research on surface waves in elastic structures done by the St. Petersburg team during 40 years is presented. By “nongeometrical phenomena” we mean those which can not be simply understood on the basis of plane wave theory but are quantitatively described by sophisticated versions of the ray method. We discuss the following phenomena: the so-called Berry phase in propagation of Rayleigh waves over a curved surface of inhomogeneous body, anomalies of polarization (as compared to the corresponding plane waves), conversion of Love and Rayleigh modes and propagation of narrow beams of surface waves. Ray theory which generalises plane wave solutions to waves with non-plane fronts is the basic tool.
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