To　improve　the　traditional　finite　element　method　based　on　potential　energy　principle,　a　finite　element　method　based　on　the　base　forces　is　proposed　by　using　explicit　expression　of　stiffness　matrices　by　Gao,　Y.C.(2003).　The　explicit　formulations　of　the　base　forces　finite　element　method　are　presented.　A　finite　element　approach　program　is　developed　by　using　MATLAB　computer　language,　which　is　used　to　solve　several　problems　of　elasticity　theory.　The　results　show　that　the　numerical　solutions　are　consistent　with　those　of　the　theoretical　solutions.