We present numerical simulations of ferroelectric switching in freely suspended smectic films. Travelling 180 degrees walls (kinks) in the film plane are quantitatively analyzed. Conditions for the formation of such walls are discussed. In addition to the conventional viscous and elastic torques and electric coupling terms to the external field, our model considers the polarization charges in the walls. The ferroelectric material interacts with the electric field produced by these charges, and the model allows for a partial screening of this field by free ionic charge carriers in the smectic film. The results of the numerical calculations are compared with electro-optic experiments performed with a polarizing microscope.