This work presents and discusses numerical results concerning the elastic post-buckling behaviour and imperfection sensitivity of regular convex polygonal cross-section (RCPS) tubular beams buckling in local, distortional and mixed local–distortional modes, a topic currently lacking research. This study is carried out in the framework of Generalised Beam Theory (GBT) geometrically non-linear analyses, enriched with a branch switching technique, and takes advantage of the GBT intrinsic modal nature to shed new light on the mechanics underlying the post-buckling behaviour of these members. Due to the small half-wavelength of all the buckling phenomena addressed, only simply supported members under uniform bending are investigated. In particular, this work investigates the post-buckling behaviour and imperfection sensitivity of RCPS beams (i) exhibiting several wall numbers (6, 8, 10, 14, 20, 30) with distinct combinations of circumradius-to-thickness ratios (ii) having distinct lengths, and (iii) containing critical-mode initial geometrical imperfections with several amplitudes. Relevant displacement profiles and modal participation diagrams are provided along trivial and non-trivial equilibrium paths, in order to draw meaningful conclusions concerning the post-buckling behaviour of RCPS tubes under bending. For comparison and validation purposes, ABAQUS shell finite element results are also presented. Display omitted •L, D and L-D post-buckling behaviours of regular polygonal tubular beams studied.•GBT non-linear analyses shed new insight on the beam post-buckling mechanics.•Beams buckling in L (D) modes exhibit plate (shell)-like post-buckling behaviours.•L-D post-buckling behaviour strongly depends on the corner displacement restraints.•Loss of uniqueness occurs along the beam D and L-D numerical equilibrium paths.