The existence of edge waves travelling along a periodic coastline cons
isting of a straight and vertical cliff face from which protrudes an i
nfinite number of identical thin barriers, each one extending througho
ut the water depth, is proved for sufficiently long barriers based on
the linear theory of water waves. The water depth is assumed to be con
stant everywhere and for this reason these edge waves are fundamentall
y different from other edge waves known in water-wave theory which all
rely on a varying bottom topography or a submerged obstacle for their
support. The proof of existence uses the modified residue-calculus me
thod and is constructive. The method provides a simple and efficient p
rocedure for the determination of the trapped-mode frequencies.