This paper presents a parts-based method for classifying scenes of 3D objects into a set of pre-determined object classes. Working at the part level, as opposed to the whole object level, enables a more flexible class representation and allows scenes in which the query object is significantly occluded to be classified. In our approach, parts are extracted from training objects and grouped into part classes using a hierarchical clustering algorithm. Each part class is represented as a collection of semi-local shape features and can be used to perform part class recognition. A mapping from part classes to object classes is derived from the learned part classes and known object classes. At run-time, a 3D query scene is sampled, local shape features are computed, and the object class is determined using the learned part classes and the part-to-object mapping. The approach is demonstrated by classifying novel 3D scenes of vehicles into eight classes.