Abstract: In the existing teaching of elastic wave theory, there is relatively little content on flexural waves, especially the lack of detailed introduction to flexural edge waves. The purpose of this paper is to fill this teaching gap and to discuss in depth the discovery history of flexural edge waves and the directions of subsequent teaching and research. Meanwhile, this paper also derives the dispersion relation of edge waves propagating along the free edge of a semi-infinite plate, and realizes the enhanced guidance of edge waves by constructing a weak stiffness strip at the free edge. With these contents, we hope to improve the theoretical system of flexural waves in the course of elastic wave theory, in order to help students have a more comprehensive understanding of this special form of flexural waves, so as to deepen their understanding of elastic waves.