Liquids handling is an important issue in biomedical analysis. Two different devices for acoustic manipulation of droplets have already been tested. The first one, more classical, uses a high frequency travelling wave and acoustic streaming. The second one uses low frequency flexural standing waves in a plate. This means of liquid handling is original and easy to implement but the physical principle is not obvious. In order to understand more precisely the phenomena involved we present new observations on droplet displacement between two planes and on the behaviour of a droplet on an inclined vibrating plane with this method. The physical principle involved is discussed. The common acoustic radiation pressure formulation is expressed via the non-linear theory of sound propagation, but in our case the acoustic wavelength is much smaller than the height of a water droplet. To get a better understanding of the phenomenon, further experiments on the internal liquid flow and behaviour of particles in the droplet have been performed. These will be compared with results obtained with particles in a thin water-filled vibrating glass tube. The general conclusion is that the phenomenon is practical to use for droplet displacement even if its complex mechanism is not completely understood.