The buckling of thin-walled structures is presented using the 1D finite element based refined beam theory formulation that permits us to obtain N-order expansions for the three displacement fields over the section domain.These higher-order models are obtained in the framework of the Carrera unified formulation(CUF).CUF is a hierarchical formulation in which the refined models are obtained with no need for ad hoc formulations.Beam theories are obtained on the basis of Taylor-type and Lagrange polynomial expansions.Assessments of these theories have been carried out by their applications to studies related to the buckling of various beam structures,like the beams with square cross section,I-section,thin rectangular cross section,and annular beams.The results obtained match very well with those from commercial finite element softwares with a significantly less computational cost.Further,various types of modes like the bending modes,axial modes,torsional modes,and circumferential shell-type modes are observed. The buckling of thin-walled structures is presented using the 1D finite element based refined beam theory formulation that permits us to obtain N-order expansions for the three displacement fields over the section domain. These higher-order models are obtained in the framework of the Carrera unified formulation (CUF). CUF is a hierarchical formulation in which the refined models are obtained with no need for ad hoc formulations. Beam theories are obtained on basis of Taylor-type and Lagrange polynomial expansions. Assessments of theseories have been carried out by their applications to studies related to the buckling of various beam structures, like the beams with square cross section, I-section, thin rectangular cross section, and annular beams.The results obtained match very well with those from commercial finite element softwares with a significant less computational cost. Future, various types of modes like the bending modes, axial modes, torsional modes, and circumferential shell-typ e modes are observed.