Abstract: An algorithm is presented for automatically creating a quadric surface model from orthographic views using the B-rep oriented approach. An edge-face-intersecting approach is developed and employed to determine the containment relationship between any two fundamental loops in each quadratic surface. A relationship-tree is then established by completing the containment test for those fundamental loops,and all candidate faces in that surface are therefore constructed by searching for the external loops and internal loops according to the relationship-tree. Further,all valid candidate faces can be assembled to compose the ultimate objects based on the characteristic of orthographic projection,the definitions and properties of 2-manifolds,and Mbius rule as well. The method not only is an important extension to the previous published algorithms for reconstructing 3D curvilinear objects from orthographic views,but also reduces the search space and improves the efficiency of the algorithm consequently by searching for face-sequences and identifying certain-face-sequences.