A face has its structural components such as eyes, nose and mouth. Availability of depth and facial shape information of a face is one of the main advantages of three-dimensional (3D) face recognition. In order to utilize the depth information, we extract rigid facial points on facial components and their relational features. We also extract shape indexes on areas around rigid points to represent curvature information of a face. We perform face recognition by using weighted distance matching, Support Vector Machine (SVM) and Independent Component Analysis (ICA) with three different sets of features. From the experimental results, the proposed feature set performs the best compared with the other feature sets for all tested classifiers. The experimental results also show that using of both the position and the curvature features can represent a face effectively and distinctively while each of them does not provide a good discrimination power for face recognition individually.