In this paper we present ELASTIFACE, a simple and versatile method for establishing correspondence between textured face models, either for the construction of a blend-shape facial rig or for the exploration of new characters by morphing between a set of input models. While there exists a wide variety of approaches for inter-surface mapping and mesh morphing, most techniques are not suitable for our application: They either require the insertion of additional vertices, are limited to topological planes or spheres, are restricted to near-isometric input meshes, and/or are algorithmically and computationally involved. In contrast, our method extends linear non-rigid registration techniques to allow for strongly varying input geometries. It is geometrically intuitive, simple to implement, computationally efficient, and robustly handles highly non-isometric input models. In order to match the requirements of other applications, such as recent perception studies, we further extend our geometric matching to the matching of input textures and morphing of geometries and rendering styles.