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The problem about a body in a three dimensional infinite channel is considered in the framework of the theory of linear water‐waves. The body has a rough surface characterized by a small parameter ε > 0 while the distance of the body to the water surface is also of order ε. Under a certain symmetry assumption, the accumulation effect for trapped mode frequencies is established, namely it is proved that, for any given  d  > 0 and integer  N  > 0, there exists a number ε ( d ,  N ) > 0 such that the problem has at least N eigenvalues in the interval (0, d) of the continuous spectrum in the case ε ∈ ( 0, ε ( d ,  N )). The corresponding eigenfunctions decay exponentially at infinity, have finite energy, and imply trapped modes.

Water‐waves modes trapped in a canal by a near‐surface rough body