3D face models accurately capture facial surfaces, making it possible for precise description of facial activities. In this paper, we present a novel mesh-based method for 3D facial expression recognition using two local shape descriptors. To characterize shape information of the local neighborhood of facial landmarks, we calculate the weighted statistical distributions of surface differential quantities, including histogram of mesh gradient (HoG) and histogram of shape index (HoS). Normal cycle theory based curvature estimation method is employed on 3D face models along with the common cubic fitting curvature estimation method for the purpose of comparison. Based on the basic fact that different expressions involve different local shape deformations, the SVM classifier with both linear and RBF kernels outperforms the state of the art results on the subset of the BU-3DFE database with the same experimental setting.