To analyze the static and dynamic behaviors of the thin-walled box girder in its lateral webs in consideration of shear lag effect and shear deformation, an approach based on the minimum potential principle is introduced in this paper. Both static and dynamic response equations as well as the corresponding natural boundary conditions of the box girder are deduced. Meanwhile, three generalized displacement functions:w(x), U(x) and 0(x) are employed and their differences in the calculus of variation are quantitatively investigated. The comparison of finite shell element results with analytical results of calculation examples validates the feasibility of the proposed approach.