We report the electric field induced thickness variations of homeotropically oriented free standing films of a smectic (C* or A*) FLCE prepared from cross - linkable ferroelectric polysiloxanes. The changes in optical path length in free standing ferroelectric liquid crystal elastomer films have been detected by means of interferometric measurements at both the first and second harmonic of the exciting electric field (w=33Hz). The measured electrostrictive strain is above 2.7% (in the thickness direction) at a electric field around 1.5 MV/m. Our experiment reveal that the inverse piezoelectric and electrostrictive response increases sharply near the Sm-C* - Sm-A* phase transition temperature. Also X-ray reflection measurements on a spin cast FLCE film reveal the constriction of smectic layers.