Abstract: We analyze the characteristics and the types of the concave structures outside the building polygons,and discuss a progressive simplification method based on the hierarchical structure of the concave.In the method,a building polygon is partitioned by constrained Delaunay TIN,and as shape primitives,triangles are used to build the concave triangle tree and to extract triangle sequence.The basic patterns of concaves are recognized by the matching of the typical sequences,which confirm and adopt the corresponding concave simplification methods.On the basis of this,the progressive simplification of complicated concaves of buildings is realized through repeating the process of recognition and simplification.The experimental results show that our method have the features of structure and progressive generalization.