As is well known, submerged horizontal cylinders can serve as waveguides for surface water waves. For large values of the wavenumber<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E1"><mml:mi>k</mml:mi></mml:math>in the direction of the cylinders, there is only one trapped wave. We construct asymptotics of these trapped modes and their frequencies as<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E2"><mml:mrow><mml:mi>k</mml:mi><mml:mo>→</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math>in the case of one or two submerged cylinders by means of reducing the initial problem to a system of integral equations on the boundaries and then solving them using a technique suggested by Zhevandrov and Merzon (2003).