The scattering of a plane sound wave normally incident on an absorbing elastic cylinder immersed in water is investigated theoretically. Because of the loss of acoustic energy due to absorption, the unitarity condition of the usualSmatrix arising from the classical resonant scattering theory fails. However, it is shown that this unitarity condition can still be met by constructing a newSmatrix which is nondiagonal. This construction is analogous to the multichannel scattering theory of particle physics. Computations are performed considering an absorbing elastic cylinder in order to check the validity of the theory.