A new hybrid numerical-analytical method is developed for the evaluati
on of the second-order velocity potential associated with bichromatic
incident waves attacking a floating long horizontal cylinder of arbitr
ary cross-section, in water of finite depth. The double sum or differe
nce frequency velocity potentials may be obtained. An analytical treat
ment of the nonhomogeneous free surface condition makes the numerical
solution accurate and efficient. The method is tested through a numeri
cal example. Results showing the difference frequency sway force and s
way response transfer function are presented for practical parameters
of a moored vessel in a multi-buoy anchorage.