Surface acoustic waves (SAWs) are one of a broad class of acoustic wave (AW) techniques that have been applied to the study of physical changes at the solid–liquid interface. Other examples include shear horizontally polarised SAWs (SH-SAWs), acoustic plate modes, Love waves and quartz crystal microbalances (QCMs). Several factors motivate and favour these techniques. The sensing surface is highly mass sensitive, it is accessible and can be chemically modified, and it provides a rapid in situ method for studying dynamic chemical and biochemical changes. Moreover, for a Newtonian fluid, the AW only entrains fluid within a penetration depth of the interface, so that the technique truly probes interfacial changes. However, many studies of liquids using these acoustic techniques have been limited to fixed pools of liquid in contact with a device surface. In this work, a damped harmonic oscillator model is described, providing a unified view of the mass damping of the shear motion in SAW, SH-SAW, and QCM AW systems by finite thickness loadings of viscoelastic fluids. The simplicity of the model also allows the effect of fluid slip at the solid–liquid interface to be examined. In the limit of small relaxation time and thick fluid coating, the model recovers the expected limit with acoustic devices acting as sensors of the device area coated by the fluid. In the large relaxation time limit, the fluid acts as an amorphous solid and the influence of the acoustic shearing motion is able to extend to the free surface of the fluid, thus inducing shear wave resonances. To complement the theory, an experiment is described which uses pulses of high frequency (169 MHz) Rayleigh SAWs to probe a small stripe of a viscous fluid (polydimethylsiloxane [PDMS] oil with a viscosity between 10 000 and 100 000 centistokes [cSt]) as it dynamically evolves in shape. The cross-sectional profile of the liquid is a well-defined spherical cap shape and this is recorded using a video based interferometry arrangement. This allows a range of geometrical parameters to be obtained and correlated with the acoustic signals. The changing geometry of the stripe does not simply decrease the magnitude of the SAW transmission as the fluid wets a progressively larger area of the surface, but also specific significant attenuations are observed. Interpreting these attenuations within the damped harmonic oscillator model, data from a range of experiments can all be fitted by relaxation rates obtained from the viscosity and a high frequency shear modulus of μ=(1.5±0.1) GN m−2. Hence, with this type of viscous fluid, the acoustic method is not acting as a simple mass sensor, although it is probing the elasticity via the shear modulus.