The exact solutions for the squeeze film flow of an incompressible Newtonian fluid and that of a gas between circular parallel surfaces are presented under the assumption of a small sinusoidal vibration. From a comparison of the conventional approximate solutions with the exact one and the experiment, it is concluded that the averaging approach in which the inertia term is averaged out across the film thickness gives fairly good approximations, and that the perturbation solution becomes remarkably inaccurate as the unsteadiness becomes high.