The distribution of polarization in thin film of multicomponent weak anisotropic ferroelectric under application of an axially symmetric electric field induced by circular electrodes is studied. We demonstrate that above a certain critical field the instability towards abrupt formation of ferroelectric vortex state appears. The polarization distribution in the vortex state exhibits a doughnut shape in agreement with experimental data. (C) 2010 Published by Elsevier B.V.