An　explicit　expression　of　element　compliance　matrix　of　the　finite　element　method　for　arbitrary　meshes　is　derived　using　the　base　forces.　The　governing　equations　expressed　by　the　base　forces　are　obtained　using　Lagrangian　multiplier　method,　and　the　displacements　formulation　of　nodes　is　given.　A　program　of　the　finite　element　method　is　developed.　The　method　is　used　to　solve　several　problems　of　arbitrary　polygonal　meshes　and　aberrant　meshes,　and　the　numerical　results　are　compared　with　those　of　the　theoretical　solutions　and　traditional　finite　element　method　solutions.　The　results　show　that　the　method　proposed　is　efficient　to　employ　the　arbitrary　meshes　and　is　free　from　mesh　aberrant.