According to the field theory of additional deformation on pre - stressed configuration , in the paper , the ordinary expression of the governing equation and variational equation of elastic buckling are brought forward . Under the theory system, through lowering dimensions, the governing equation and variational equation for the critical condition solution of elastic buckling of a plane arch are deduced, and the eigenvalues problem of the linear homogeneous differential equations corresponding to the equations are concluded While Abandoning the plane assumption and considering shearing deformation, the linear finite element method arithmetic of bending bar's cross section containing six degree of freedom is given. The process of derivation and calculational results show that, under this system info, the finite element equations of bending bar deduced are accurate and easy to be used to numeric calculations, and the conclusion achieved is more practical.