Consider a moving surface, on which the time derivatives of velocity and pressure are discontinuous but on which the velocity and pressure themselves are continuous. Such discontinuities may correspond to dissipated shock waves or “weak shocks.” Then under the assumption that each moving fluid element undergoes adiabatic changes, it can be shown that the surface is given by the solution of a generalized eikonal equation, which in the case of a fluid at rest becomes the ordinary eikonal equation of ray acoustics. This treatment does not require the usual assumption of infinitesimal amplitudes ordinarily used in acoustics. Conservation laws corresponding to those in ray theory are also derived under the above assumptions.