Abstract: Aiming at the incomplete application of materials in elastic-plastic stage. In this paper, by using the principle of elastic-plastic partition minimum potential energy, thecriterion of potential energy and Euler equation of bending straight beam under linear strengthening model are derived. The deflection curve equation of cantilever beam and simply supported beam under concentrated load issolved. The deflection curve equation is put into Matlab software for numerical calculation, and the results are compared with ANSYS. The results show that both the numerical solution and the finite element value meet the allowable error range in practical engineering. The proposed method provides a new idea for solving practical engineering problems.