This paper proposes a deformation technique called Planar Bones, derived from Surface-oriented Free Form Deformations, and explores its application to the context of Facial Animation. The warping method proposed uses as the control input a polygonal mesh, which is built as a triangulation of the Feature Points defined by MPEG-4. A strong correspondence between the facial geometry and this control structure is maintained throughout the animation, overcoming the issues of many of the current systems defined using this standard.