The problem of wave propagation along the tip of a slender elastic wedge immersed in liquid is considered. Interaction between wedge mode and acoustic waves is studied. Namely, attenuation of the wedge wave occurs if the velocity of the wedge mode is greater than the velocity of the acoustic waves and the wedge mode velocity changes in the opposite case. A functional–differential equation is derived for the problem. This equation is solved asymptotically by using the Wiener–Hopf method in the case of very light liquid loading.