We present a brief review of dispersion characteristics of normal modes in an elastic slab and a cylinder. Key topics of the 125-year history of the problem and its modern reflection in the global information space are elucidated. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 2, pp. 86–104, April–June, 2008.
Meleshko, V. V., Bondarenko, A. A., Dovgiy, S. A., Trofimchuck, A. N., & Heijst, van, G. J. F. (2009). Elastic waveguides : history and the state of art.I. Journal of Mathematical Sciences, 162(1), 99-120. https://doi.org/10.1007/s10958-009-9623-8