Based　on　the　edge-based　smoothed　FEM　(ES-FEM)　and　the　partition　of　unity,　the　first　major　items　of　Williams＇　series　for　the　displacement　field　near　the　crack　tip　are　incorporated　in　the　test　and　trial　function　space,　resulting　in　the　enriched　ES-FEM　formulation,　eEF-FEM.　The　eES-FEM　does　not　differentiate　any　shape　functions,　avoiding　the　treatment　of　the　1/r　singularity　in　computing　the　stiffness　matrix.　The　complexity　of　computation　is　accordingly　reduced.　Meanwhile,　it　is　pointed　out　that　the　variational　foundation　of　the　eES-FEM　is　the　generalized　Galerkin　method.　Typical　numerical　examples　are　analyzed,　suggesting　that　the　results　of　the　eES-FEM　are　much　better　than　either　FEM　or　ES-FEM.