Using　the　concept　of　base　forces　as　state　variables,　a　new　finite　element　method　-　the　base　force　element　method　(BFEM)　on　complementary　energy　principle　for　linear　elasticity　problems　is　presented.　Firstly,　an　explicit　expression　of　compliance　matrix　for　an　element　is　derived　through　base　forces　by　dyadic　vectors.　Then,　the　explicit　control　equations　of　finite　element　method　of　complementary　energy　principle　are　derived　using　Lagrange　multiplier　method.　Thereafter,　the　base　forces　element　procedure　for　linear　elasticity　is　developed.　Finally,　several　examples　are　analyzed　to　illustrate　the　reliability　and　accuracy　of　the　formulation　and　the　procedure.