Abstract: Three modes for refining finite element meshes locally are proposed‚in which meshes are refined near the key-point‚in the circle area or in the rectangle area．In the embedded regions that are constructed for refined meshes generation‚an algorithm based on Delaunay triangulation is then employed for the generation of graded meshes．In this algorithm‚nodes and elements are generated dynamically and simultaneously‚and the refined meshes generated in the embedded regions are embedded into the original meshes．As a result‚meshes are refined in the key areas．Examples show that the meshes refined by the proposed method are of good quality and can satisfy the requirements of finite element analysis． 

Key words: finite element, mesh generation, local refinement, Delaunay triangulation