This paper presents a classification scheme for 3D block-shaped parts. A part is block-shaped if the contours of its orthographic projections are all rectangles. A block-shaped part is classified based on its partitioned view-contours, which are the result of partitioning the contours of its orthographic projections by visible or invisible projected line segments. The regions and their adjacency in a partitioned view-contour are first converted to a graph, then to a reference tree, and finally to a vector form, with which a back-propagation neural network classifier can be trained and applied. The proposed back-propagation neural network classifier is in a cascaded structure and has advantages that each network can be limited to a small size and trained independently. Based on the classification results on their partitioned view-contours, parts are grouped into families that can be in one of the three levels of similarity. Extensive empirical tests have been performed; the pros and cons of the approach are also investigated.