Abstract: In the theory of elasticity, when dealing with the fixed boundary conditions of beams, the displacement expression based on the integration of strain component is usually complex, which is difficult to accurately meet the fixed boundary conditions, so only an approximate solution can be obtained. In this paper, the displacement constraint of the midpoint of the fixed boundary is adopted, and the fixed boundary condition is redefined combined with the least squares method, so as to realize the accurate solution of the displacement of the beam. By comparing the differences of four typical formulas of boundary conditions, it is helpful for students to flexibly grasp the simplification methods of the fixed boundary conditions and provide materials for research-based teaching.