A three-dimensional constitutive model for polarization switching in ferroelectric materials is used to predict the formation of switching zones in an atomic force microscopy(AFM) tip/ferroelectric thin film/bottom electrode system via finite element simulation. Initially the ferrolectric film is poled upward and the bottom electrode is grounded. A strong dc field is imposed on a fixed point of the top surface of the film through the AFM tip. A small switching zone with downward polarization is nucleated and grows with time. It is found that initially the shape of the switched zone is that of a bulgy dagger, but later turn to the shape of a reversed cup with the lower part wider than the upper part. It can also be concluded that the size of switching zones increases with the period of applied electric potential. The present results are qualitatively consistent with experimental observations.