This paper addresses the problem of 3D face recognition using spherical sparse representations. We first propose a fully automated registration process that permits to align the 3D face point clouds. These point clouds are then represented as signals on the 2D sphere, in order to take benefit of the geometry information. Simultaneous sparse approximations implement a dimensionality reduction process by subspace projection. Each face is typically represented by a few spherical basis functions that are able to capture the salient facial characteristics. The dimensionality reduction step preserves the discriminant facial information and eventually permits an effective matching in the reduced space, where it can further be combined with LDA for improved recognition performance. We evaluate the 3D face recognition algorithm on the FRGC v.1.0 data set, where it outperforms classical state-of-the-art solutions based on PCA or LDA on depth face images.