The body force was incorporated into the immiscible, binary fluid model of Orlandini et al. [9] and the combined model was used to simulate interfacial waves. The gravitational density of the two fluids can be changed by applying the body force with different strengths to each fluid. Standing waves were initialised at the fluid interface, with a given wavelength and amplitude, without any prior knowledge of the other properties of the wave. This means that measurements taken from the standing waves, at a later time, are in no way influenced by any velocity or oscillation imposed on the wave during the initialisation procedure. A large number of standing waves were simulated for a range of the available model and wave parameters. The frequency of the waves, the rate at which they are damped and the velocities produced by the wave motion were all recorded at selected times for each of the waves studied. Progressive waves were also simulated. These were initialised using the results obtain for standing waves under the same conditions. The frequency, damping parameter and velocities were measured for the progressive waves and found to be in agreement with those obtained for the standing wave simulations.