One of the basic properties of thin ferroelectric films is the ability to switch polarization under the influence of an external electric field. The application of such thin films as memory devices is based on this phenomenon. The switching process of the thin films has some distinctive features. These include, for example, the dependence of the switching time on the electrode surface and an anomalous variation of the switching time curve with the amplitude of bipolar rectangular electric voltage impulses. To describe the physical nature of these peculiarities a simple model is developed. The qualitative compatibility between experiment and the model is shown on the basis of the Pb(Zr,Ti,B’,B")O3 (PZT)-type thin films with the chemical constitution Pb(Zr0.53Ti0.45W0.01Cd0.01)O3.