In this chapter a summary of the equations governing internal wave motion is presented. Initially wave propagation at a sharp interface, between two non-viscous fluids, will be considered and the equations describing the wave motion derived. Two fluids with a finite smooth interface will also be considered and the effect of the finite interface on the equations of motion discussed. The fluid viscosity will also be examined and its effect on the frequency, the damping of interfacial waves and the velocity profile will be found. Finally the equations for standing waves will be found from the progressive wave solutions.