This paper is devoted to cellular beams manufactured by flame cutting and welding of hot rolled I-sections. The influence of fabrication processes on the size of geometric and material imperfections was considered. Static performance was characterised, as were the failure modes, with particular emphasis on the Vierendeel mechanism and web-post buckling. As the literature review shows, a local loss of web post stability is a frequent failure mode of cellular beam with closely spaced web openings. The main objective of this paper is present a summary of research on web post buckling (WPB) in cellular beams in light of the available analytical computational methods for determining WPB resistance based on the analogy to compression member buckling. This paper addresses the need for a clear assessment of the discrepancies between the assumptions and calculation algorithms used in the presented methods, so far lacking in the literature. This paper includes an explanation of the essence of the WPB phenomenon, a summary of the basic assumptions and algorithms used in the available methods, a description of the differences between them, and a critical comparison of these methods. The presented algorithms were unified and adjusted to the nomenclature of PN-EN 1993-1-1. For 7 cellular beams, the analytical column buckling resistance under the action of vertical shear force was determined according to 5 analytical methods implemented in MS Excel. The results were presented in tabular and graphical forms. Significant discrepancies between the results from the different methods were shown and discussed. The assumptions of the methods vary significantly. The largest differences between the predicted resistances were observed for narrow posts, while for wider posts, the methods showed better agreement. The lack of clear consensus on the correct design procedure does not encourage designers to optimally design such load-bearing members or may lead to construction disasters. This article indicates the points of disagreement concerning the calculation models used and outlines the direction for further work. A step for future work will be to verify the assumptions of numerical models and establish clear guidelines for designers in the field of analytical calculations.