Shape description and recognition is an important and interesting problem in scene analysis. Our approach to shape description is a formal model of a shape consisting of a set of primitives, their properties, and their interrelationships. The primitives are the simple parts and intrusions of the shape which can be derived through the graph-theoretic clustering procedure described in [31]. The interrelationships are two ternary relations on the primitives: the intrusion relation which relates two simple parts that join to the intrusion they surround and the protrusion relation which relates two intrusions to the protrusion between them. Using this model, a shape matching procedure that uses a tree search with look-ahead to find mappings from a prototype shape to a candidate shape has been developed. An experimental SNOBOL4 implementation has been used to test the program on hand-printed character data with favorable results.