Abstract: Based on the work reciprocal theorem, the minimum potential energy principle and the principle of the minimum potential action of the dual mixed variable of the displacement and the stress are used to solve the problem of the deformation and the stability of a straight beam with large deflection. The results are compared with the finite element simulation results to verify the feasibility of the proposed method and the accuracy of the calculation results. The method is simple and flexible, and the result is accurate. It provides a new solution to solve the problem of a straight beam with large deflection. It can be directly applied to practical engineering problems.