Abstract: An algorithm for constructing PEBI mesh of arbitrarily shaped and constrained planar domains was presented. When it acted on polygonal domain, all the vertices of boundary edges and scattered points within the domain were sorted in scan man-ner. Each time a feasible vertex was taken to generate a new triangle on known edge, then scanning these triangles which didn't
meet the Delaunay rule in these new triangles and continually dealt with them until the whole domain is triangulated. Finally, connecting each circumcircle center of these triangles, PEBI mesh~generated. Elasticity smoothing and swapping diagonal of quadrilateral methods were applied to locally optimize the cell form.By plan mapping, It could be applied to 3D mesh of reservoir. Ap-
placation of the method was proven that it was practicable.

Key words: PEBI mesh, algorithm, triangulation, mesh generation