We present an algorithm for 3D face deformation and modeling using range data captured by a 3D scanner. Using only three facial feature points extracted from the range images and a 3D generic face model, the algorithm first aligns the 3D model to the entire range data of a given subject's face. Then each aligned triangle of the mesh model, with three vertices, is treated as a surface plane which is then fitted to the corresponding interior 3D range data, using least squares plane fitting. Via triangular vertices subdivisions, a higher resolution model is generated from the coordinates of the aligned and fitted model. Finally the model and its triangular surfaces are fitted once again resulting in a smoother mesh model that resembles and captures the surface characteristic of the face. Application of the final deformed model in 3D face recognition, using a publicly available database, shows promising results.