In order to study the reasonable warping displacement function of shear lag of box girder, plate flange is regarded in this paper as an elastic body connected by a spring with certain stiffness in longitudinal parallel and a flange plate spring model is established according to the longitudinal force and deformation characteristics of flange plate of box girder. And based on energy variational principle, flange plate equilibrium differential equation is established, deducing that the longitudinal displacement function is a linear combination of hyperbolic function and triangular function. The warping displacement function is determined as three single forms:hyperbolic sinusoidal function, hyperbolic cosine function and sinusoidal function. By substituting three function forms into the shear lag variational equation, the bending normal stress equations of the three longitudinal displacement functions are obtained. In order to verify the rationality of the three functions derived from the theory, the normal stress of flange plate calculated by the three functions is compared with the measured value, the calculated value in the form of cubic parabola, and the calculated value of solid finite element. The effect of different function forms on the stress distribution of flange plate is analyzed from the perspective of the function property. The results show that the calculated value of sinusoidal function is in good agreement with the measured value and the calculated value of solid finite element method. In addition, the second derivative of the function is positively correlated with the stress distribution of the flange plate.