In [1, 2], we observed an effect of decreasing prop-agation velocity of longitudinal sound waves in a fineelastic rod after its immersion in a liquid. The decreasein the sound velocity is governed by the so-calledboundary layer of the liquid, which vibrates togetherwith the rod as an associated mass. The thickness ofthis layer depends on both the vibration frequency andboth the density and viscosity of the liquid. At a soundsignal frequency of about 100 kHz, the typical value ofthe boundary layer thickness for technical oils is 10 to50 µ m [1]. Therefore, the decrease in the sound veloc-ity is considerable only for thin samples, i.e., sampleswhose thickness does not exceed a few hundreds ofmicrons.Since the thickness of the boundary layer dependson the viscosity of a liquid, it is appropriate to employthe above effect for determining the viscosity. Anadvantage of this method is the possibility of perform-ing high-rate viscosity measurements that attain a rateof up to several thousands per second. Such high ratesmake it possible to measure the viscosity even in thecase when it varies with time.The problem of the effect of a liquid on the propa-gation velocity and the damping of acoustic waves in athin strip immersed into an infinite volume of a liquidwas solved analytically [1]. However, there exists theproblem of controlling the behavior of polymeric resinsdeposited in liquid form on a metal surface and solidi-fied on it.The goal of this study is to theoretically solve theproblem related to the propagation of a longitudinalharmonic acoustic wave in a thin elastic strip coated bya layer of an incompressible Newtonian liquid.We introduce a system of coordinates such that thefree surface of a liquid coincides with the plane X = 0.The longitudinal vibrations of the elastic strip along the Y -axis are described by the equation [3–5] (1) Here, u is the displacement of a small strip elementfrom the equilibrium position; ρ