In this paper, we introduce a novel method of automatically finding the training set of RBF networks for morphing a prototype face to represent a new face. This is done by automatically specifying and adjusting corresponding feature points on a target face. The RBF networks are then used to transfer the muscles on the prototype face to the morphed face. The automatic adjusting of the feature points on the target face is done by Genetic Algorithms. The fitness function used in the GA expresses the difference between the surface of the morphed face and the target face. We also present an algorithm to calculate this function fast. KEY WORDS Facial Animation, Geometric Modelling, Radial Basis Functions, Genetic Algorithms