On the basis of the symmetry consideration of the Sc* phase, a generalized elastic free energy of ferroelectric Sc* liquid crystals is presented to account for the layer compression or dilatation and the layer distortion as well ascdirector deformation. The present elastic free energy is expressed in terms of three vectors, i.e. thecdirector and the wave vector and the spontaneous polarization vector. According to the present Sc* model withC2symmetry, it is shown that there may exist 17 non-chiral, 4 chiral terms and 14 flexoelectric terms in the Sc* phase. A few practical applications are also presented to elucidate some interesting elastic properties of Sc* (or Sc) in simplifed geometries.