Using　the　concept　of　base　forces,　the　problem　on　the　explicit　tensor　expression　of　element　stiffness　matrix　for　finite　element　method　was　identified,　mathematic　model　of　finite　element　method　on　potential　energy　principle　was　established　by　using　an　explicit　expression.　A　code　on　the　base　forces　finite　element　method　was　developed　by　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.　The　availability　of　this　approach　is　verified.