In this paper, the boundary conformability of 3D constrained Delaunay triangulat ion is analyzed. Based on the theory of Delaunay triangulation, the feasibility of 3D constrained Delaunay triangulation is discussed emphatically. The algorith m of 3D constrained Delaunay triangulation of finite domain is designed. Applica tions in oil and geological exploration and mechanical part design are illustrat ed. The algorithm plays an important role in the computation and analysis of com plicated objects.