Based　on　the　concept　of　the　base　forces　by　Gao,　a　new　finite　element　method-the　base　force　element　method　(BFEM)　on　complementary　energy　principle　for　two-dimensional　geometrically　nonlinear　problems　is　presented　using　arbitrary　meshes.　An　arbitrary　convex　polygonal　element　model　of　the　BFEM　for　geometrically　nonlinear　problem　is　derived　by　assuming　that　the　stress　is　uniformly　distributed　on　each　edges　of　a　plane　element.　The　explicit　formulations　of　the　control　equations　for　the　BFEM　are　derived　using　the　modified　complementary　energy　principle.　The　BFEM　is　naturally　universal　for　small　displacement　and　large　displacement　problems.　A　number　of　example　problems　are　solved　using　the　BFEM　and　the　results　are　compared　with　corresponding　analytical　solutions.　A　good　agreement　of　the　results　using　the　arbitrary　convex　polygonal　element　model　of　BFEM　in　the　large　displacement　and　large　rotation　calculations,　are　observed.　(C)　2013　Elsevier　B.V.　All　rights　reserved.