Using　the　concept　of　base　forces,　the　problem　of　the　explicit　tensor　expression　of　the　element　stiffness　matrix　for　a　new　finite　element　method　(FEM)-the　base　force　element　method　(BFEM)　was　studied.　The　mathematic　model　of　the　BFEM　on　potential　energy　principle　was　established　by　using　an　explicit　expression.　A　code　for　the　BFEM　was　developed　using　MATLAB　computer　language.　The　approach　was　used　to　solve　several　problems　of　elasticity　theory,　and　various　shape　elements　were　compared　and　analyzed.　The　numerical　results　are　consistent　with　those　of　the　theoretical　solutions,　and　the　applicability　of　this　approach　is　verified.