Abstract: As a simple component, the beam is widely used in engineering. in the classical beam theory, a modification factor and an equilibrium of the internal forces are introduced to obtain the shear stress, which makes the process complicated. In this paper, a displacement function of Legendre polynomials is proposed to analyze the shear stress with consideration of the conditions of zero transverse shear stress at the top and the bottom. The excellent agreement between the theoretical results and those obtained by the finite element method shows that the theoretical model of Legendre polynomials is capable of determining the shear stress of the beam accurately. Therefore, the method may provide a new theoretical reference for the mechanics analysis of the beam.