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Nonplanar surfaces are often encountered in engineering structures. In aerospace structures, periodically corrugated boundaries are formed by friction-stir-welding. In civil engineering structures, rebars used in reinforced concrete beams and slabs have periodic surface. Periodic structures are also being used to create desired acoustic band gaps. For health monitoring of these structures, a good understanding of the elastic wave propagation through such periodic structures is necessary. Although a number of research papers on the wave propagation in periodic structures are available in the literature, no one experimentally investigated the guided wave propagation through plates with periodic boundaries and compared the experimental results with theoretical predictions as done in this paper. The experimental results clearly show that elastic waves can propagate through the corrugated plate (waveguide) for certain frequencies called “pass bands,” and find it difficult to propagate for some other frequencies called “stop bands.” Stop bands are found to increase with the degree of corrugation. Experimental results are compared with the theoretical predictions, and good matching is observed for plates with small degree of corrugation. Only two parameters—the depth of corrugation and the wavelength of the periodicity—are sufficient for modeling the elastic wave propagation in slightly corrugated plates.