Compared　with　the　Euler　beam　theory,　the　Timoshenko　beam　theory　has　the　advantages　in　solution　accuracy　and　in　applicable　aspect　ratios.　However,　it　received　some　criticisms　in　two　aspects:　firstly,　it　is　energy　inconsistent,　and　secondly,　it　cannot　be　reduced　to　the　Euler　beam　theory　in　a　mechanics　way.　From　the　reduced　standpoint　of　the　higher-order　displacement　mode,　the　two　lower-order　beam　theories　endowed　with　a　linear　axial　displacement　are　systematically　studied.　The　present　work　shows　that　the　shear　free　Euler　beam　theory　is　different　from　the　first-order　shear　deformable　beam　theory　because　they　are　basded　on　different　conditions,　and　hence　they　cannot　be　mutually　transformed.　Thus,　it　is　uncecessary　to　reduce　the　Timoshenko　beam　theory,　which　poses　as　an　improved　first-order　shear　deformable　beam　theory,　to　the　Euler　beam　theory.　The　lower-order　beam　theory　is　derived　on　the　assumption　of　the　higher-order　displacement　mode,　and　the　physical　essence　is　revealed　that,　irrespective　of　the　displacement　mode,　the　Timoshenko　beam　theory　is　in　essence　such　a　lower-order　beam　theory.　©　2018,　Science　Press.　All　right　reserved.