We develop a Rayleigh-type approach to the analysis of compressible granular flow. In this approach, a (possibly negative) influx of energy from the walls is taken into account. This is greatly advantageous in granular flow rheology, since such influx of energy arises spontaneously as soon as the balance between the energy influx (due to whatever mechanism keeps the unperturbed system in a thermalized state) and the dissipation rate is violated. We show that standing waves, although waves of a rather peculiar type, may well exist, and that such waves have thicknesses of several hundreds particle diameters. We also give an analysis of the stability of compressible granular flow, which exhibits some peculiar characteristics.