As is well-known, submerged horizontal cylinders can serve as waveguides for surface water waves. For large values of the wavenumber k in the direction of cylinder, there is only one trapped wave. We construct asymptotics of these trapped modes and their frequencies as  in the case of one submerged cylinder by means of reducing the initial problem to a system of integral equations on the boundaries and then solving them using a scheme suggested by Zhevandrov and Merzon [13].

asymptotics, eigenvalues, trapped water waves.