Abstract: Comparison and analysis are performed for two typical theories with distortion angle and distortion deflection as displacement parameters. Their results are proved to be identical. The conversion between distortion deflection and distortion angle is established by use of the displacement coordination of cross-section frame, and the conversion functions for the governing differential equations of both theories are derived. Based on the generalized coordinate principle, an explicit definition is given for the distortion centre and displacement modes are determined, and then an analytical theory is presented using energy variational principle, which sufficiently takes account of shear deformation. The formats of initial parameters are deduced to solve the presented differential equations. The influence of shear deformation is investigated and the results show that shear deformation affect insignificantly the distortion warping stress and transverse bending stress.