The main goal of this paper is to illustrate a geometric analysis of 3D facial shapes in the presence of varying facial expressions. This approach consists of the following two main steps: (1) Each facial surface is automatically denoised and preprocessed to result in an indexed collection of facial curves. During this step, one detects the tip of the nose and defines a surface distance function with that tip as the reference point. The level curves of this distance function are the desired facial curves. (2) Comparisons between faces are based on optimal deformations from one to another. This, in turn, is based on optimal deformations of the corresponding facial curves across surfaces under an elastic metric. The experimental results, generated using a subset of the Face Recognition Grand Challenge v2 data set, demonstrate the success of the proposed framework in recognizing people under different facial expressions. The recognition rates obtained here exceed those for a baseline ICP algorithm on the same data set.