This paper prrsents shape matching of two-dimensional object. This shape matching is applied to two-dimensional simple c10sedcurves represented by polygons. A large number of shape matching procedures have proposed baseed on teh view that shape can be represented by a vector of numerical features, and that this representation can be matched using techniques from statical pattern recognition. The varieties of features that have been extracted from shapes and used to represent them are numerous. But all of these feature-based approches suffer from the shortcoming that the descriptor of a segment of a shape do not ordinarily bear any simple relations hip to the description for the entire shape. We solve the segment matching problem of shape matching, defined as the recognition of a piece of a shape as approximate match to a part of large shape, by using relaxation labeling technique.