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The propagation of Rayleigh waves along solid surfaces has attracted great attention due to its ubiquity in seismic waves, non-destructive evaluation, acoustic surface wave devices, and so on. Moreover, Rayleigh waves in periodic structures and their related band gaps caused by Bragg resonances have also been investigated. In this paper, we theoretically and experimentally demonstrate the propagation mechanism of Rayleigh waves along the side wall of a periodically corrugated aluminum plate. As expected, the band gap structures are observed in the spectrum of Rayleigh waves. However, not all the band gaps are caused by the Bragg resonances. The additional band gaps created by the interference of different transverse modes are observed. Different from the well-known Bragg resonance, the different mode interference, producing stronger energy attenuation and wider band gap, is called non-Bragg resonances. The two resonances can be manipulated by varying the phase shift of two sidewall corrugations, achieving an effective prohibition of Rayleigh wave propagation. These findings on Rayleigh wave propagation in periodic structures provide a comprehensive understanding of wave-structure interactions, which can be used to regulate elastic waves in various applications, such as multifunctional elastic wave separators, filters, and modulators.